Advanced Search

Maple 2024 Questions and Posts

These are Posts and Questions associated with the product, Maple 2024
View unanswered posts
Maple 2024 Questions and Posts Feed

How to plot a vector with units and one without un...

Asked by: FDS 190
vector units plotting
1 hour ago
0  0

Dear Power Users,

This is probably a simple question for you but I am stuck. In the attached worksheet I would like to plot (the plot is called P5) a vector with units (mm) against a vector without units. This didn't work out, so I removed the units from the vector with units, and this plotted but after the conversion the numeric values are no longer in mm but inches. How can I correct this?

Thank you in advance for your time and willingness to help.

testSheetHorseShoe.mw

How Plotting function without singularity?...

Asked by: salim-barzani 1410
parameters plotting
Yesterday at 2:54 AM
0  3

in some of my function i have a big problem which i can't plot thus function even i know what is the shape of plot, i have two type of ploting directly giving parameter and using explor but for this kind of plot we can't use explor so i have to give the function directly parameter but is wasting my time a lot and i can't get my plot even spending a days by changing parameter one by one, my questions is this how i can plot this kind of function without bieng a singular i need this function to be non singular is not importan about the parameter can be any number 
thanks for any help 

plots-long_term_.mw

the shape of plot must be like this but must have two of them 

Display a simple plane...

Asked by: Ronan 1336
3d plane plotting
May 18 2025
0  13

This seems rediculous to have to ask. I just want to display a plane. The plot is used in other plots so I gave it a name. I get "length of output exceed 1000000" and the plot does not display. I then have to "display" the plot name "display(plt0)" to see it. I had tried geom3d but found if infuriating, (maybe I am missing something there).

An I missing something simple here?

restart

NULL

with(plots)

pln := x-2*y+3*z

x-2*y+3*z

 (1)

NULL

display(implicitplot3d(pln, x = -3 .. 3, y = -3 .. 3, z = -3 .. 3, style = patchnogrid, transparency = .6))

  

NULL

NULL

plt0 := display(implicitplot3d(pln, x = -3 .. 3, y = -3 .. 3, z = -3 .. 3, style = patchnogrid, transparency = .6))

`[Length of output exceeds limit of 1000000]`

 (2)

display(plt0)

  

Intended use

NULL

Download 2025-05-18_Q_display_a_simple_plane.mw

There is any way for knowing which parameter are r...

Asked by: salim-barzani 1410
solve ode parameters
May 18 2025
1  0

I'm currently working on applying a specific method to solve a nonlinear equation. However, I've encountered a recurring issue: during the process, I often cannot determine certain parameters, which forces me to abandon the solution or switch to a different method. This has happened multiple times and is disrupting my goal of applying all intended methods consistently to a single equation.

In particular, I’m struggling to identify the correct parameters for U(ξ), which are essential for the solution. This challenge is not limited to one method I’ve faced similar problems in previous attempts, and I’m unsure why these parameters cannot be derived in some cases.

My question is: How can I manage this issue effectively? Is there a reliable way to predict or determine whether the necessary parameters will emerge correctly before fully applying a method?

I would greatly appreciate any insights or strategies you could share to help me handle this problem more systematically.

Thank you in advance for your support.

runing.mw

How can I simplify a symbolic number?...

Asked by: Saalehorizontale 55
simplify symbolic rootof
May 16 2025
1  8

Hey guys, 

I am solving big systems of equations and doing some other stuff with the results. So now I got two diffrent ways and it turns out, that the give back the same result but they present it in diffrent ways. So my quesion now is, how can I simplify a symbolic number to its shortest form. In my example you can see, that the diffrence of y_1 and y_2 is 0, so they describe the same number. However y_2 is a way more complicated expression. So here I know the easier expression, but what if I dont. What is the right command to force maple to find a simplier expression for y_2? I read about evala but its doent do the job as you can see in the attached file. I also tryd things like simplify, normal, expand but it didint worked out too. simplify_symbolic_numbers.mw

> 

restart; y_1 := RootOf(_Z^5-2*_Z^4+9*_Z^3-14*_Z^2+9*_Z-2, .4687 .. .4727); y_2 := 2*RootOf(2*_Z^5-9*_Z^4+14*_Z^3-9*_Z^2+2*_Z-1, 2.109 .. 2.118)^4-9*RootOf(2*_Z^5-9*_Z^4+14*_Z^3-9*_Z^2+2*_Z-1, 2.109 .. 2.118)^3+14*RootOf(2*_Z^5-9*_Z^4+14*_Z^3-9*_Z^2+2*_Z-1, 2.109 .. 2.118)^2-9*RootOf(2*_Z^5-9*_Z^4+14*_Z^3-9*_Z^2+2*_Z-1, 2.109 .. 2.118)+2; evala(Normal(y_1-y_2)); evala(y_2)

0

  

2*RootOf(2*_Z^5-9*_Z^4+14*_Z^3-9*_Z^2+2*_Z-1, 2.109 .. 2.118)^4-9*RootOf(2*_Z^5-9*_Z^4+14*_Z^3-9*_Z^2+2*_Z-1, 2.109 .. 2.118)^3+14*RootOf(2*_Z^5-9*_Z^4+14*_Z^3-9*_Z^2+2*_Z-1, 2.109 .. 2.118)^2-9*RootOf(2*_Z^5-9*_Z^4+14*_Z^3-9*_Z^2+2*_Z-1, 2.109 .. 2.118)+2

 (1)
 

NULL

Download simplify_symbolic_numbers.mw

Thank you for your help. Regards, Felix

Identifying the Corresponding Solution Class for D...

Asked by: salim-barzani 1410
ode differential-equations duplicate-question
May 16 2025
2  2

I am working on obtaining the complete set of solutions for a given ordinary differential equation (ODE). While testing various cases from the auxiliary ODE method, I derived a solution of the form U(ξ). However, I am currently unable to determine which specific case or class from the established solution set this result corresponds to.

I would appreciate any guidance or method to correctly classify each obtained solution U(ξ) according to its respective case within the set of auxiliary ODE cases.

ode.mw

Guidance on replacement???...

Asked by: delvin 60
ode substitution differential-equations
May 16 2025
1  4

 Hi,

How can I replace all the expressions diff(G(xi), xi)/G(xi) with the new variable w(xi) in the next step? (Even the ones that have powers)

NULL

> 

eq2 := c*a0*(-lambda*diff(G(xi), xi) - mu*G(xi))/G(xi) - c*a0*diff(G(xi), xi)^2/G(xi)^2 - alpha*a0*diff(G(xi), xi)/((1 - 2*f(sqrt(lambda^2 - 4*mu)*y)*diff(G(xi), xi)/(sqrt(epsilon*lambda^2 - 4*epsilon*mu)*G(xi)) - f(sqrt(lambda^2 - 4*mu)*y)*lambda/sqrt(epsilon*lambda^2 - 4*epsilon*mu))*G(xi)) - alpha*a0*lambda/(2*(1 - 2*f(sqrt(lambda^2 - 4*mu)*y)*diff(G(xi), xi)/(sqrt(epsilon*lambda^2 - 4*epsilon*mu)*G(xi)) - f(sqrt(lambda^2 - 4*mu)*y)*lambda/sqrt(epsilon*lambda^2 - 4*epsilon*mu))) + alpha*a0*sqrt(epsilon*lambda^2 - 4*epsilon*mu)*epsilon*f(sqrt(lambda^2 - 4*mu)*y)/(2*(1 - 2*f(sqrt(lambda^2 - 4*mu)*y)*diff(G(xi), xi)/(sqrt(epsilon*lambda^2 - 4*epsilon*mu)*G(xi)) - f(sqrt(lambda^2 - 4*mu)*y)*lambda/sqrt(epsilon*lambda^2 - 4*epsilon*mu))) + alpha*a0*diff(G(xi), xi)/((1 + 2*f(sqrt(lambda^2 - 4*mu)*y)*diff(G(xi), xi)/(sqrt(epsilon*lambda^2 - 4*epsilon*mu)*G(xi)) + f(sqrt(lambda^2 - 4*mu)*y)*lambda/sqrt(epsilon*lambda^2 - 4*epsilon*mu))*G(xi)) + alpha*a0*lambda/(2*(1 + 2*f(sqrt(lambda^2 - 4*mu)*y)*diff(G(xi), xi)/(sqrt(epsilon*lambda^2 - 4*epsilon*mu)*G(xi)) + f(sqrt(lambda^2 - 4*mu)*y)*lambda/sqrt(epsilon*lambda^2 - 4*epsilon*mu))) + alpha*a0*sqrt(epsilon*lambda^2 - 4*epsilon*mu)*epsilon*f(sqrt(lambda^2 - 4*mu)*y)/(2*(1 + 2*f(sqrt(lambda^2 - 4*mu)*y)*diff(G(xi), xi)/(sqrt(epsilon*lambda^2 - 4*epsilon*mu)*G(xi)) + f(sqrt(lambda^2 - 4*mu)*y)*lambda/sqrt(epsilon*lambda^2 - 4*epsilon*mu))) - beta*a0^2*diff(G(xi), xi)^2/(G(xi)^2*(1 - 2*f(sqrt(lambda^2 - 4*mu)*y)*diff(G(xi), xi)/(sqrt(epsilon*lambda^2 - 4*epsilon*mu)*G(xi)) - f(sqrt(lambda^2 - 4*mu)*y)*lambda/sqrt(epsilon*lambda^2 - 4*epsilon*mu))) - beta*a0^2*diff(G(xi), xi)*lambda/(2*(1 - 2*f(sqrt(lambda^2 - 4*mu)*y)*diff(G(xi), xi)/(sqrt(epsilon*lambda^2 - 4*epsilon*mu)*G(xi)) - f(sqrt(lambda^2 - 4*mu)*y)*lambda/sqrt(epsilon*lambda^2 - 4*epsilon*mu))*G(xi)) + beta*a0^2*diff(G(xi), xi)*sqrt(epsilon*lambda^2 - 4*epsilon*mu)*epsilon*f(sqrt(lambda^2 - 4*mu)*y)/(2*(1 - 2*f(sqrt(lambda^2 - 4*mu)*y)*diff(G(xi), xi)/(sqrt(epsilon*lambda^2 - 4*epsilon*mu)*G(xi)) - f(sqrt(lambda^2 - 4*mu)*y)*lambda/sqrt(epsilon*lambda^2 - 4*epsilon*mu))*G(xi)) + beta*a0^2*diff(G(xi), xi)^2/(G(xi)^2*(1 + 2*f(sqrt(lambda^2 - 4*mu)*y)*diff(G(xi), xi)/(sqrt(epsilon*lambda^2 - 4*epsilon*mu)*G(xi)) + f(sqrt(lambda^2 - 4*mu)*y)*lambda/sqrt(epsilon*lambda^2 - 4*epsilon*mu))) + beta*a0^2*diff(G(xi), xi)*lambda/(2*(1 + 2*f(sqrt(lambda^2 - 4*mu)*y)*diff(G(xi), xi)/(sqrt(epsilon*lambda^2 - 4*epsilon*mu)*G(xi)) + f(sqrt(lambda^2 - 4*mu)*y)*lambda/sqrt(epsilon*lambda^2 - 4*epsilon*mu))*G(xi)) + beta*a0^2*diff(G(xi), xi)*sqrt(epsilon*lambda^2 - 4*epsilon*mu)*epsilon*f(sqrt(lambda^2 - 4*mu)*y)/(2*(1 + 2*f(sqrt(lambda^2 - 4*mu)*y)*diff(G(xi), xi)/(sqrt(epsilon*lambda^2 - 4*epsilon*mu)*G(xi)) + f(sqrt(lambda^2 - 4*mu)*y)*lambda/sqrt(epsilon*lambda^2 - 4*epsilon*mu))*G(xi)) - gamma*a0^3*diff(G(xi), xi)^3/(G(xi)^3*(1 - 2*f(sqrt(lambda^2 - 4*mu)*y)*diff(G(xi), xi)/(sqrt(epsilon*lambda^2 - 4*epsilon*mu)*G(xi)) - f(sqrt(lambda^2 - 4*mu)*y)*lambda/sqrt(epsilon*lambda^2 - 4*epsilon*mu))) - gamma*a0^3*diff(G(xi), xi)^2*lambda/(2*G(xi)^2*(1 - 2*f(sqrt(lambda^2 - 4*mu)*y)*diff(G(xi), xi)/(sqrt(epsilon*lambda^2 - 4*epsilon*mu)*G(xi)) - f(sqrt(lambda^2 - 4*mu)*y)*lambda/sqrt(epsilon*lambda^2 - 4*epsilon*mu))) + gamma*a0^3*diff(G(xi), xi)^2*sqrt(epsilon*lambda^2 - 4*epsilon*mu)*epsilon*f(sqrt(lambda^2 - 4*mu)*y)/(2*G(xi)^2*(1 - 2*f(sqrt(lambda^2 - 4*mu)*y)*diff(G(xi), xi)/(sqrt(epsilon*lambda^2 - 4*epsilon*mu)*G(xi)) - f(sqrt(lambda^2 - 4*mu)*y)*lambda/sqrt(epsilon*lambda^2 - 4*epsilon*mu))) + gamma*a0^3*diff(G(xi), xi)^3/(G(xi)^3*(1 + 2*f(sqrt(lambda^2 - 4*mu)*y)*diff(G(xi), xi)/(sqrt(epsilon*lambda^2 - 4*epsilon*mu)*G(xi)) + f(sqrt(lambda^2 - 4*mu)*y)*lambda/sqrt(epsilon*lambda^2 - 4*epsilon*mu))) + gamma*a0^3*diff(G(xi), xi)^2*lambda/(2*G(xi)^2*(1 + 2*f(sqrt(lambda^2 - 4*mu)*y)*diff(G(xi), xi)/(sqrt(epsilon*lambda^2 - 4*epsilon*mu)*G(xi)) + f(sqrt(lambda^2 - 4*mu)*y)*lambda/sqrt(epsilon*lambda^2 - 4*epsilon*mu))) + gamma*a0^3*diff(G(xi), xi)^2*sqrt(epsilon*lambda^2 - 4*epsilon*mu)*epsilon*f(sqrt(lambda^2 - 4*mu)*y)/(2*G(xi)^2*(1 + 2*f(sqrt(lambda^2 - 4*mu)*y)*diff(G(xi), xi)/(sqrt(epsilon*lambda^2 - 4*epsilon*mu)*G(xi)) + f(sqrt(lambda^2 - 4*mu)*y)*lambda/sqrt(epsilon*lambda^2 - 4*epsilon*mu)));

c*a0*(-lambda*(diff(G(xi), xi))-mu*G(xi))/G(xi)-c*a0*(diff(G(xi), xi))^2/G(xi)^2-alpha*a0*(diff(G(xi), xi))/((1-2*f((lambda^2-4*mu)^(1/2)*y)*(diff(G(xi), xi))/((epsilon*lambda^2-4*epsilon*mu)^(1/2)*G(xi))-f((lambda^2-4*mu)^(1/2)*y)*lambda/(epsilon*lambda^2-4*epsilon*mu)^(1/2))*G(xi))-alpha*a0*lambda/(2-4*f((lambda^2-4*mu)^(1/2)*y)*(diff(G(xi), xi))/((epsilon*lambda^2-4*epsilon*mu)^(1/2)*G(xi))-2*f((lambda^2-4*mu)^(1/2)*y)*lambda/(epsilon*lambda^2-4*epsilon*mu)^(1/2))+alpha*a0*(epsilon*lambda^2-4*epsilon*mu)^(1/2)*epsilon*f((lambda^2-4*mu)^(1/2)*y)/(2-4*f((lambda^2-4*mu)^(1/2)*y)*(diff(G(xi), xi))/((epsilon*lambda^2-4*epsilon*mu)^(1/2)*G(xi))-2*f((lambda^2-4*mu)^(1/2)*y)*lambda/(epsilon*lambda^2-4*epsilon*mu)^(1/2))+alpha*a0*(diff(G(xi), xi))/((1+2*f((lambda^2-4*mu)^(1/2)*y)*(diff(G(xi), xi))/((epsilon*lambda^2-4*epsilon*mu)^(1/2)*G(xi))+f((lambda^2-4*mu)^(1/2)*y)*lambda/(epsilon*lambda^2-4*epsilon*mu)^(1/2))*G(xi))+alpha*a0*lambda/(2+4*f((lambda^2-4*mu)^(1/2)*y)*(diff(G(xi), xi))/((epsilon*lambda^2-4*epsilon*mu)^(1/2)*G(xi))+2*f((lambda^2-4*mu)^(1/2)*y)*lambda/(epsilon*lambda^2-4*epsilon*mu)^(1/2))+alpha*a0*(epsilon*lambda^2-4*epsilon*mu)^(1/2)*epsilon*f((lambda^2-4*mu)^(1/2)*y)/(2+4*f((lambda^2-4*mu)^(1/2)*y)*(diff(G(xi), xi))/((epsilon*lambda^2-4*epsilon*mu)^(1/2)*G(xi))+2*f((lambda^2-4*mu)^(1/2)*y)*lambda/(epsilon*lambda^2-4*epsilon*mu)^(1/2))-beta*a0^2*(diff(G(xi), xi))^2/(G(xi)^2*(1-2*f((lambda^2-4*mu)^(1/2)*y)*(diff(G(xi), xi))/((epsilon*lambda^2-4*epsilon*mu)^(1/2)*G(xi))-f((lambda^2-4*mu)^(1/2)*y)*lambda/(epsilon*lambda^2-4*epsilon*mu)^(1/2)))-(1/2)*beta*a0^2*(diff(G(xi), xi))*lambda/((1-2*f((lambda^2-4*mu)^(1/2)*y)*(diff(G(xi), xi))/((epsilon*lambda^2-4*epsilon*mu)^(1/2)*G(xi))-f((lambda^2-4*mu)^(1/2)*y)*lambda/(epsilon*lambda^2-4*epsilon*mu)^(1/2))*G(xi))+(1/2)*beta*a0^2*(diff(G(xi), xi))*(epsilon*lambda^2-4*epsilon*mu)^(1/2)*epsilon*f((lambda^2-4*mu)^(1/2)*y)/((1-2*f((lambda^2-4*mu)^(1/2)*y)*(diff(G(xi), xi))/((epsilon*lambda^2-4*epsilon*mu)^(1/2)*G(xi))-f((lambda^2-4*mu)^(1/2)*y)*lambda/(epsilon*lambda^2-4*epsilon*mu)^(1/2))*G(xi))+beta*a0^2*(diff(G(xi), xi))^2/(G(xi)^2*(1+2*f((lambda^2-4*mu)^(1/2)*y)*(diff(G(xi), xi))/((epsilon*lambda^2-4*epsilon*mu)^(1/2)*G(xi))+f((lambda^2-4*mu)^(1/2)*y)*lambda/(epsilon*lambda^2-4*epsilon*mu)^(1/2)))+(1/2)*beta*a0^2*(diff(G(xi), xi))*lambda/((1+2*f((lambda^2-4*mu)^(1/2)*y)*(diff(G(xi), xi))/((epsilon*lambda^2-4*epsilon*mu)^(1/2)*G(xi))+f((lambda^2-4*mu)^(1/2)*y)*lambda/(epsilon*lambda^2-4*epsilon*mu)^(1/2))*G(xi))+(1/2)*beta*a0^2*(diff(G(xi), xi))*(epsilon*lambda^2-4*epsilon*mu)^(1/2)*epsilon*f((lambda^2-4*mu)^(1/2)*y)/((1+2*f((lambda^2-4*mu)^(1/2)*y)*(diff(G(xi), xi))/((epsilon*lambda^2-4*epsilon*mu)^(1/2)*G(xi))+f((lambda^2-4*mu)^(1/2)*y)*lambda/(epsilon*lambda^2-4*epsilon*mu)^(1/2))*G(xi))-gamma*a0^3*(diff(G(xi), xi))^3/(G(xi)^3*(1-2*f((lambda^2-4*mu)^(1/2)*y)*(diff(G(xi), xi))/((epsilon*lambda^2-4*epsilon*mu)^(1/2)*G(xi))-f((lambda^2-4*mu)^(1/2)*y)*lambda/(epsilon*lambda^2-4*epsilon*mu)^(1/2)))-(1/2)*gamma*a0^3*(diff(G(xi), xi))^2*lambda/(G(xi)^2*(1-2*f((lambda^2-4*mu)^(1/2)*y)*(diff(G(xi), xi))/((epsilon*lambda^2-4*epsilon*mu)^(1/2)*G(xi))-f((lambda^2-4*mu)^(1/2)*y)*lambda/(epsilon*lambda^2-4*epsilon*mu)^(1/2)))+(1/2)*gamma*a0^3*(diff(G(xi), xi))^2*(epsilon*lambda^2-4*epsilon*mu)^(1/2)*epsilon*f((lambda^2-4*mu)^(1/2)*y)/(G(xi)^2*(1-2*f((lambda^2-4*mu)^(1/2)*y)*(diff(G(xi), xi))/((epsilon*lambda^2-4*epsilon*mu)^(1/2)*G(xi))-f((lambda^2-4*mu)^(1/2)*y)*lambda/(epsilon*lambda^2-4*epsilon*mu)^(1/2)))+gamma*a0^3*(diff(G(xi), xi))^3/(G(xi)^3*(1+2*f((lambda^2-4*mu)^(1/2)*y)*(diff(G(xi), xi))/((epsilon*lambda^2-4*epsilon*mu)^(1/2)*G(xi))+f((lambda^2-4*mu)^(1/2)*y)*lambda/(epsilon*lambda^2-4*epsilon*mu)^(1/2)))+(1/2)*gamma*a0^3*(diff(G(xi), xi))^2*lambda/(G(xi)^2*(1+2*f((lambda^2-4*mu)^(1/2)*y)*(diff(G(xi), xi))/((epsilon*lambda^2-4*epsilon*mu)^(1/2)*G(xi))+f((lambda^2-4*mu)^(1/2)*y)*lambda/(epsilon*lambda^2-4*epsilon*mu)^(1/2)))+(1/2)*gamma*a0^3*(diff(G(xi), xi))^2*(epsilon*lambda^2-4*epsilon*mu)^(1/2)*epsilon*f((lambda^2-4*mu)^(1/2)*y)/(G(xi)^2*(1+2*f((lambda^2-4*mu)^(1/2)*y)*(diff(G(xi), xi))/((epsilon*lambda^2-4*epsilon*mu)^(1/2)*G(xi))+f((lambda^2-4*mu)^(1/2)*y)*lambda/(epsilon*lambda^2-4*epsilon*mu)^(1/2)))

 (1)

NULL

Download 123.mw

Page print formating problem Maple 2024...

Asked by: Ronan 1336
pdf export table
May 15 2025
0  3

I have a print format problem in Maple 2024.  For documents I print out, I use a special layout where all the contents are inside a table. The table is rigged to print on A4 paper. This is useful for my math notes. I havent done this for 18+ months. There appears to be a bug in Maple 2024. Only the first page is printed. Things work ok in Maple 2023. Maybe it is a setting difference or corruption in my install. Could somebody confirm this. Also if you can reproduce the problem could you let me know if it is in Maple 2025. I haven't upgraded yet.

 

2025-05-15_Q_page_print_formating.mw 
2025-05-15_Q_page_print_formating_M_2023.pdf
2025-05-15_Q_page_print_formating_M_2024.pdf

how to find posint solution of a specified equatio...

Asked by: Aixleft math 120
factorial
May 15 2025
0  4

Hi! how to find posint solution of this equation?

Is factorial move fast so that cannot solve?

any advice is appreciated.

> 

restart
> 

NULL
> 

eq := `assuming`([factorial(x)+1 = y^2], [x::posint, y::posint])

factorial(x)+1 = y^2

 (1)
> 

`assuming`([solve(eq, {x, y})], [x <= 100, y <= 100])

{x = RootOf(factorial(_Z)-y^2+1), y = y}

 (2)
 

NULL

Download find_posint_.mw

how to decompose a rational fraction into simple...

Asked by: Blanc 20
modp rational-function edited-question
May 12 2025
1  13

Hello,
Can you tell me how to decompose a rational fraction into simple elements in Fp?

Thank you.

How determine number of condition and inf it then ...

Asked by: salim-barzani 1410
ode substitution differential-equations
May 09 2025
3  8

i seperate my equation of real part and imaginary part i want  after taking integrale from my real part we see the pattern betwen real and imaginary part  which they equal about variable beside coefficient , i want to determine and find parameter from real part of my equation then substitute in imaginary for solving but  the number of condition i don't know is how much and there is a little bit repeatation how i can determine the correct one and then substitute ?

> 

restart
> 

with(PDEtools)
> 

undeclare(prime, quiet)
> 

declare(u(x, t), quiet); declare(U(xi), quiet); declare(V(xi), quiet)
> 

pde := I*(diff(u(x, t), `$`(t, 2))-s^2*(diff(u(x, t), `$`(x, 2))))+(1/24)*c[1]*(diff(u(x, t), t, `$`(x, 4)))-alpha*s*c[1]*(diff(u(x, t), `$`(x, 5)))+diff(c[2]*u(x, t)*U(-t*v+x)^2, t)-beta*s*(diff(c[2]*u(x, t)*U(-t*v+x)^2, x))

I*(diff(diff(u(x, t), t), t)-s^2*(diff(diff(u(x, t), x), x)))+(1/24)*c[1]*(diff(diff(diff(diff(diff(u(x, t), t), x), x), x), x))-alpha*s*c[1]*(diff(diff(diff(diff(diff(u(x, t), x), x), x), x), x))+c[2]*(diff(u(x, t), t))*U(-t*v+x)^2-2*c[2]*u(x, t)*U(-t*v+x)*(D(U))(-t*v+x)*v-beta*s*(c[2]*(diff(u(x, t), x))*U(-t*v+x)^2+2*c[2]*u(x, t)*U(-t*v+x)*(D(U))(-t*v+x))

 (1)
> 

G1 := U(-t*v+x) = U(xi); G2 := (D(U))(-t*v+x) = diff(U(xi), xi); G3 := ((D@@2)(U))(-t*v+x) = diff(U(xi), `$`(xi, 2)); G4 := ((D@@3)(U))(-t*v+x) = diff(U(xi), `$`(xi, 3)); G5 := ((D@@4)(U))(-t*v+x) = diff(U(xi), `$`(xi, 4)); G6 := ((D@@5)(U))(-t*v+x) = diff(U(xi), `$`(xi, 5))
> 

T := xi = -t*v+x; T1 := u(x, t) = U(-t*v+x)*exp(I*k*(t*w+x))

xi = -t*v+x

  

u(x, t) = U(-t*v+x)*exp(I*k*(t*w+x))

 (2)
> 

P1 := I*(diff(u(x, t), `$`(t, 2))-s^2*(diff(u(x, t), `$`(x, 2))))+(1/24)*c[1]*(diff(u(x, t), t, `$`(x, 4)))-alpha*s*c[1]*(diff(u(x, t), `$`(x, 5)))+diff(c[2]*u(x, t)*U(-t*v+x)^2, t)-beta*s*(diff(c[2]*u(x, t)*U(-t*v+x)^2, x))

I*(diff(diff(u(x, t), t), t)-s^2*(diff(diff(u(x, t), x), x)))+(1/24)*c[1]*(diff(diff(diff(diff(diff(u(x, t), t), x), x), x), x))-alpha*s*c[1]*(diff(diff(diff(diff(diff(u(x, t), x), x), x), x), x))+c[2]*(diff(u(x, t), t))*U(-t*v+x)^2-2*c[2]*u(x, t)*U(-t*v+x)*(D(U))(-t*v+x)*v-beta*s*(c[2]*(diff(u(x, t), x))*U(-t*v+x)^2+2*c[2]*u(x, t)*U(-t*v+x)*(D(U))(-t*v+x))

 (3)
> 

P11 := eval(P1, {T, T1})

I*(((D@@2)(U))(-t*v+x)*v^2*exp(I*k*(t*w+x))-(2*I)*(D(U))(-t*v+x)*v*k*w*exp(I*k*(t*w+x))-U(-t*v+x)*k^2*w^2*exp(I*k*(t*w+x))-s^2*(((D@@2)(U))(-t*v+x)*exp(I*k*(t*w+x))+(2*I)*(D(U))(-t*v+x)*k*exp(I*k*(t*w+x))-U(-t*v+x)*k^2*exp(I*k*(t*w+x))))+(1/24)*c[1]*(-((D@@5)(U))(-t*v+x)*v*exp(I*k*(t*w+x))+(4*I)*((D@@2)(U))(-t*v+x)*v*k^3*exp(I*k*(t*w+x))+I*U(-t*v+x)*k^5*w*exp(I*k*(t*w+x))+6*((D@@3)(U))(-t*v+x)*v*k^2*exp(I*k*(t*w+x))-(4*I)*((D@@4)(U))(-t*v+x)*v*k*exp(I*k*(t*w+x))-(6*I)*((D@@2)(U))(-t*v+x)*k^3*w*exp(I*k*(t*w+x))-(D(U))(-t*v+x)*v*k^4*exp(I*k*(t*w+x))+I*((D@@4)(U))(-t*v+x)*k*w*exp(I*k*(t*w+x))-4*((D@@3)(U))(-t*v+x)*k^2*w*exp(I*k*(t*w+x))+4*(D(U))(-t*v+x)*k^4*w*exp(I*k*(t*w+x)))-alpha*s*c[1]*(((D@@5)(U))(-t*v+x)*exp(I*k*(t*w+x))+(5*I)*((D@@4)(U))(-t*v+x)*k*exp(I*k*(t*w+x))-10*((D@@3)(U))(-t*v+x)*k^2*exp(I*k*(t*w+x))-(10*I)*((D@@2)(U))(-t*v+x)*k^3*exp(I*k*(t*w+x))+5*(D(U))(-t*v+x)*k^4*exp(I*k*(t*w+x))+I*U(-t*v+x)*k^5*exp(I*k*(t*w+x)))+c[2]*(-(D(U))(-t*v+x)*v*exp(I*k*(t*w+x))+I*U(-t*v+x)*k*w*exp(I*k*(t*w+x)))*U(-t*v+x)^2-2*c[2]*U(-t*v+x)^2*exp(I*k*(t*w+x))*(D(U))(-t*v+x)*v-beta*s*(c[2]*((D(U))(-t*v+x)*exp(I*k*(t*w+x))+I*U(-t*v+x)*k*exp(I*k*(t*w+x)))*U(-t*v+x)^2+2*c[2]*U(-t*v+x)^2*exp(I*k*(t*w+x))*(D(U))(-t*v+x))

 (4)
> 

P111 := subs({G1, G2, G3, G4, G5, G6}, P11)

I*((diff(diff(U(xi), xi), xi))*v^2*exp(I*k*(t*w+x))-(2*I)*(diff(U(xi), xi))*v*k*w*exp(I*k*(t*w+x))-U(xi)*k^2*w^2*exp(I*k*(t*w+x))-s^2*((diff(diff(U(xi), xi), xi))*exp(I*k*(t*w+x))+(2*I)*(diff(U(xi), xi))*k*exp(I*k*(t*w+x))-U(xi)*k^2*exp(I*k*(t*w+x))))+(1/24)*c[1]*(-(diff(diff(diff(diff(diff(U(xi), xi), xi), xi), xi), xi))*v*exp(I*k*(t*w+x))+(4*I)*(diff(diff(U(xi), xi), xi))*v*k^3*exp(I*k*(t*w+x))+I*U(xi)*k^5*w*exp(I*k*(t*w+x))+6*(diff(diff(diff(U(xi), xi), xi), xi))*v*k^2*exp(I*k*(t*w+x))-(4*I)*(diff(diff(diff(diff(U(xi), xi), xi), xi), xi))*v*k*exp(I*k*(t*w+x))-(6*I)*(diff(diff(U(xi), xi), xi))*k^3*w*exp(I*k*(t*w+x))-(diff(U(xi), xi))*v*k^4*exp(I*k*(t*w+x))+I*(diff(diff(diff(diff(U(xi), xi), xi), xi), xi))*k*w*exp(I*k*(t*w+x))-4*(diff(diff(diff(U(xi), xi), xi), xi))*k^2*w*exp(I*k*(t*w+x))+4*(diff(U(xi), xi))*k^4*w*exp(I*k*(t*w+x)))-alpha*s*c[1]*((diff(diff(diff(diff(diff(U(xi), xi), xi), xi), xi), xi))*exp(I*k*(t*w+x))+(5*I)*(diff(diff(diff(diff(U(xi), xi), xi), xi), xi))*k*exp(I*k*(t*w+x))-10*(diff(diff(diff(U(xi), xi), xi), xi))*k^2*exp(I*k*(t*w+x))-(10*I)*(diff(diff(U(xi), xi), xi))*k^3*exp(I*k*(t*w+x))+5*(diff(U(xi), xi))*k^4*exp(I*k*(t*w+x))+I*U(xi)*k^5*exp(I*k*(t*w+x)))+c[2]*(-(diff(U(xi), xi))*v*exp(I*k*(t*w+x))+I*U(xi)*k*w*exp(I*k*(t*w+x)))*U(xi)^2-2*c[2]*U(xi)^2*exp(I*k*(t*w+x))*(diff(U(xi), xi))*v-beta*s*(c[2]*((diff(U(xi), xi))*exp(I*k*(t*w+x))+I*U(xi)*k*exp(I*k*(t*w+x)))*U(xi)^2+2*c[2]*U(xi)^2*exp(I*k*(t*w+x))*(diff(U(xi), xi)))

 (5)
> 

pde1 := P111 = 0

I*((diff(diff(U(xi), xi), xi))*v^2*exp(I*k*(t*w+x))-(2*I)*(diff(U(xi), xi))*v*k*w*exp(I*k*(t*w+x))-U(xi)*k^2*w^2*exp(I*k*(t*w+x))-s^2*((diff(diff(U(xi), xi), xi))*exp(I*k*(t*w+x))+(2*I)*(diff(U(xi), xi))*k*exp(I*k*(t*w+x))-U(xi)*k^2*exp(I*k*(t*w+x))))+(1/24)*c[1]*(-(diff(diff(diff(diff(diff(U(xi), xi), xi), xi), xi), xi))*v*exp(I*k*(t*w+x))+(4*I)*(diff(diff(U(xi), xi), xi))*v*k^3*exp(I*k*(t*w+x))+I*U(xi)*k^5*w*exp(I*k*(t*w+x))+6*(diff(diff(diff(U(xi), xi), xi), xi))*v*k^2*exp(I*k*(t*w+x))-(4*I)*(diff(diff(diff(diff(U(xi), xi), xi), xi), xi))*v*k*exp(I*k*(t*w+x))-(6*I)*(diff(diff(U(xi), xi), xi))*k^3*w*exp(I*k*(t*w+x))-(diff(U(xi), xi))*v*k^4*exp(I*k*(t*w+x))+I*(diff(diff(diff(diff(U(xi), xi), xi), xi), xi))*k*w*exp(I*k*(t*w+x))-4*(diff(diff(diff(U(xi), xi), xi), xi))*k^2*w*exp(I*k*(t*w+x))+4*(diff(U(xi), xi))*k^4*w*exp(I*k*(t*w+x)))-alpha*s*c[1]*((diff(diff(diff(diff(diff(U(xi), xi), xi), xi), xi), xi))*exp(I*k*(t*w+x))+(5*I)*(diff(diff(diff(diff(U(xi), xi), xi), xi), xi))*k*exp(I*k*(t*w+x))-10*(diff(diff(diff(U(xi), xi), xi), xi))*k^2*exp(I*k*(t*w+x))-(10*I)*(diff(diff(U(xi), xi), xi))*k^3*exp(I*k*(t*w+x))+5*(diff(U(xi), xi))*k^4*exp(I*k*(t*w+x))+I*U(xi)*k^5*exp(I*k*(t*w+x)))+c[2]*(-(diff(U(xi), xi))*v*exp(I*k*(t*w+x))+I*U(xi)*k*w*exp(I*k*(t*w+x)))*U(xi)^2-2*c[2]*U(xi)^2*exp(I*k*(t*w+x))*(diff(U(xi), xi))*v-beta*s*(c[2]*((diff(U(xi), xi))*exp(I*k*(t*w+x))+I*U(xi)*k*exp(I*k*(t*w+x)))*U(xi)^2+2*c[2]*U(xi)^2*exp(I*k*(t*w+x))*(diff(U(xi), xi))) = 0

 (6)
> 

numer(lhs(pde1))*denom(rhs(pde1)) = numer(rhs(pde1))*denom(lhs(pde1))

-exp(I*k*(t*w+x))*((diff(U(xi), xi))*k^4*v*c[1]-4*(diff(U(xi), xi))*k^4*w*c[1]-48*(diff(U(xi), xi))*k*v*w+72*c[2]*U(xi)^2*(diff(U(xi), xi))*v-6*(diff(diff(diff(U(xi), xi), xi), xi))*k^2*v*c[1]+4*(diff(diff(diff(U(xi), xi), xi), xi))*k^2*w*c[1]+24*(diff(diff(diff(diff(diff(U(xi), xi), xi), xi), xi), xi))*alpha*s*c[1]-(24*I)*U(xi)*k^2*s^2+(24*I)*U(xi)*k^2*w^2+(24*I)*U(xi)*alpha*k^5*s*c[1]-(240*I)*(diff(diff(U(xi), xi), xi))*alpha*k^3*s*c[1]+(24*I)*U(xi)^3*beta*k*s*c[2]+(120*I)*(diff(diff(diff(diff(U(xi), xi), xi), xi), xi))*alpha*k*s*c[1]+120*(diff(U(xi), xi))*alpha*k^4*s*c[1]+72*(diff(U(xi), xi))*U(xi)^2*beta*s*c[2]-240*(diff(diff(diff(U(xi), xi), xi), xi))*alpha*k^2*s*c[1]-I*U(xi)*k^5*w*c[1]-(4*I)*(diff(diff(U(xi), xi), xi))*k^3*v*c[1]+(6*I)*(diff(diff(U(xi), xi), xi))*k^3*w*c[1]-(24*I)*U(xi)^3*k*w*c[2]+(4*I)*(diff(diff(diff(diff(U(xi), xi), xi), xi), xi))*k*v*c[1]-I*(diff(diff(diff(diff(U(xi), xi), xi), xi), xi))*k*w*c[1]-48*(diff(U(xi), xi))*k*s^2+(diff(diff(diff(diff(diff(U(xi), xi), xi), xi), xi), xi))*v*c[1]+(24*I)*(diff(diff(U(xi), xi), xi))*s^2-(24*I)*(diff(diff(U(xi), xi), xi))*v^2) = 0

 (7)
> 

%/(-exp(I*k*(t*w+x)))

(diff(U(xi), xi))*k^4*v*c[1]-4*(diff(U(xi), xi))*k^4*w*c[1]-48*(diff(U(xi), xi))*k*v*w+72*c[2]*U(xi)^2*(diff(U(xi), xi))*v-6*(diff(diff(diff(U(xi), xi), xi), xi))*k^2*v*c[1]+4*(diff(diff(diff(U(xi), xi), xi), xi))*k^2*w*c[1]+24*(diff(diff(diff(diff(diff(U(xi), xi), xi), xi), xi), xi))*alpha*s*c[1]-(24*I)*U(xi)*k^2*s^2+(24*I)*U(xi)*k^2*w^2+(24*I)*U(xi)*alpha*k^5*s*c[1]-(240*I)*(diff(diff(U(xi), xi), xi))*alpha*k^3*s*c[1]+(24*I)*U(xi)^3*beta*k*s*c[2]+(120*I)*(diff(diff(diff(diff(U(xi), xi), xi), xi), xi))*alpha*k*s*c[1]+120*(diff(U(xi), xi))*alpha*k^4*s*c[1]+72*(diff(U(xi), xi))*U(xi)^2*beta*s*c[2]-240*(diff(diff(diff(U(xi), xi), xi), xi))*alpha*k^2*s*c[1]-I*U(xi)*k^5*w*c[1]-(4*I)*(diff(diff(U(xi), xi), xi))*k^3*v*c[1]+(6*I)*(diff(diff(U(xi), xi), xi))*k^3*w*c[1]-(24*I)*U(xi)^3*k*w*c[2]+(4*I)*(diff(diff(diff(diff(U(xi), xi), xi), xi), xi))*k*v*c[1]-I*(diff(diff(diff(diff(U(xi), xi), xi), xi), xi))*k*w*c[1]-48*(diff(U(xi), xi))*k*s^2+(diff(diff(diff(diff(diff(U(xi), xi), xi), xi), xi), xi))*v*c[1]+(24*I)*(diff(diff(U(xi), xi), xi))*s^2-(24*I)*(diff(diff(U(xi), xi), xi))*v^2 = 0

 (8)
> 

Re(%)

Re((diff(U(xi), xi))*k^4*v*c[1]-4*(diff(U(xi), xi))*k^4*w*c[1]-48*(diff(U(xi), xi))*k*v*w+72*c[2]*U(xi)^2*(diff(U(xi), xi))*v-6*(diff(diff(diff(U(xi), xi), xi), xi))*k^2*v*c[1]+4*(diff(diff(diff(U(xi), xi), xi), xi))*k^2*w*c[1]+24*(diff(diff(diff(diff(diff(U(xi), xi), xi), xi), xi), xi))*alpha*s*c[1]+120*(diff(U(xi), xi))*alpha*k^4*s*c[1]+72*(diff(U(xi), xi))*U(xi)^2*beta*s*c[2]-240*(diff(diff(diff(U(xi), xi), xi), xi))*alpha*k^2*s*c[1]-48*(diff(U(xi), xi))*k*s^2+(diff(diff(diff(diff(diff(U(xi), xi), xi), xi), xi), xi))*v*c[1])-Im(-24*U(xi)*k^2*s^2+24*U(xi)*k^2*w^2+24*U(xi)*alpha*k^5*s*c[1]-240*(diff(diff(U(xi), xi), xi))*alpha*k^3*s*c[1]+24*U(xi)^3*beta*k*s*c[2]+120*(diff(diff(diff(diff(U(xi), xi), xi), xi), xi))*alpha*k*s*c[1]-U(xi)*k^5*w*c[1]-4*(diff(diff(U(xi), xi), xi))*k^3*v*c[1]+6*(diff(diff(U(xi), xi), xi))*k^3*w*c[1]-24*U(xi)^3*k*w*c[2]+4*(diff(diff(diff(diff(U(xi), xi), xi), xi), xi))*k*v*c[1]-(diff(diff(diff(diff(U(xi), xi), xi), xi), xi))*k*w*c[1]+24*(diff(diff(U(xi), xi), xi))*s^2-24*(diff(diff(U(xi), xi), xi))*v^2) = 0

 (9)
> 

R := (diff(U(xi), xi))*k^4*v*c[1]-4*(diff(U(xi), xi))*k^4*w*c[1]-48*(diff(U(xi), xi))*k*v*w+72*c[2]*U(xi)^2*(diff(U(xi), xi))*v-6*(diff(diff(diff(U(xi), xi), xi), xi))*k^2*v*c[1]+4*(diff(diff(diff(U(xi), xi), xi), xi))*k^2*w*c[1]+24*(diff(diff(diff(diff(diff(U(xi), xi), xi), xi), xi), xi))*alpha*s*c[1]+120*(diff(U(xi), xi))*alpha*k^4*s*c[1]+72*(diff(U(xi), xi))*U(xi)^2*beta*s*c[2]-240*(diff(diff(diff(U(xi), xi), xi), xi))*alpha*k^2*s*c[1]-48*(diff(U(xi), xi))*k*s^2+(diff(diff(diff(diff(diff(U(xi), xi), xi), xi), xi), xi))*v*c[1] = 0

(diff(U(xi), xi))*k^4*v*c[1]-4*(diff(U(xi), xi))*k^4*w*c[1]-48*(diff(U(xi), xi))*k*v*w+72*c[2]*U(xi)^2*(diff(U(xi), xi))*v-6*(diff(diff(diff(U(xi), xi), xi), xi))*k^2*v*c[1]+4*(diff(diff(diff(U(xi), xi), xi), xi))*k^2*w*c[1]+24*(diff(diff(diff(diff(diff(U(xi), xi), xi), xi), xi), xi))*alpha*s*c[1]+120*(diff(U(xi), xi))*alpha*k^4*s*c[1]+72*(diff(U(xi), xi))*U(xi)^2*beta*s*c[2]-240*(diff(diff(diff(U(xi), xi), xi), xi))*alpha*k^2*s*c[1]-48*(diff(U(xi), xi))*k*s^2+(diff(diff(diff(diff(diff(U(xi), xi), xi), xi), xi), xi))*v*c[1] = 0

 (10)
> 

collect(R, {U(xi), diff(U(xi), xi), diff(U(xi), `$`(xi, 3)), diff(diff(U(xi), xi), xi), diff(diff(diff(diff(diff(U(xi), xi), xi), xi), xi), xi)})

(72*beta*s*c[2]+72*v*c[2])*(diff(U(xi), xi))*U(xi)^2+(120*alpha*k^4*s*c[1]+k^4*v*c[1]-4*k^4*w*c[1]-48*k*s^2-48*k*v*w)*(diff(U(xi), xi))+(-240*alpha*k^2*s*c[1]-6*k^2*v*c[1]+4*k^2*w*c[1])*(diff(diff(diff(U(xi), xi), xi), xi))+(24*alpha*s*c[1]+v*c[1])*(diff(diff(diff(diff(diff(U(xi), xi), xi), xi), xi), xi)) = 0

 (11)
> 

map(int, (72*beta*s*c[2]+72*v*c[2])*(diff(U(xi), xi))*U(xi)^2+(120*alpha*k^4*s*c[1]+k^4*v*c[1]-4*k^4*w*c[1]-48*k*s^2-48*k*v*w)*(diff(U(xi), xi))+(-240*alpha*k^2*s*c[1]-6*k^2*v*c[1]+4*k^2*w*c[1])*(diff(diff(diff(U(xi), xi), xi), xi))+(24*alpha*s*c[1]+v*c[1])*(diff(diff(diff(diff(diff(U(xi), xi), xi), xi), xi), xi)) = 0, xi)

(24*alpha*s*c[1]+v*c[1])*(diff(diff(diff(diff(U(xi), xi), xi), xi), xi))+(-240*alpha*k^2*s*c[1]-6*k^2*v*c[1]+4*k^2*w*c[1])*(diff(diff(U(xi), xi), xi))+(120*alpha*k^4*s*c[1]+k^4*v*c[1]-4*k^4*w*c[1]-48*k*s^2-48*k*v*w)*U(xi)+(1/3)*(72*beta*s*c[2]+72*v*c[2])*U(xi)^3 = 0

 (12)
> 

numer(lhs((24*alpha*s*c[1]+v*c[1])*(diff(diff(diff(diff(U(xi), xi), xi), xi), xi))+(-240*alpha*k^2*s*c[1]-6*k^2*v*c[1]+4*k^2*w*c[1])*(diff(diff(U(xi), xi), xi))+(120*alpha*k^4*s*c[1]+k^4*v*c[1]-4*k^4*w*c[1]-48*k*s^2-48*k*v*w)*U(xi)+(1/3)*(72*beta*s*c[2]+72*v*c[2])*U(xi)^3 = 0))*denom(rhs((24*alpha*s*c[1]+v*c[1])*(diff(diff(diff(diff(U(xi), xi), xi), xi), xi))+(-240*alpha*k^2*s*c[1]-6*k^2*v*c[1]+4*k^2*w*c[1])*(diff(diff(U(xi), xi), xi))+(120*alpha*k^4*s*c[1]+k^4*v*c[1]-4*k^4*w*c[1]-48*k*s^2-48*k*v*w)*U(xi)+(1/3)*(72*beta*s*c[2]+72*v*c[2])*U(xi)^3 = 0)) = numer(rhs((24*alpha*s*c[1]+v*c[1])*(diff(diff(diff(diff(U(xi), xi), xi), xi), xi))+(-240*alpha*k^2*s*c[1]-6*k^2*v*c[1]+4*k^2*w*c[1])*(diff(diff(U(xi), xi), xi))+(120*alpha*k^4*s*c[1]+k^4*v*c[1]-4*k^4*w*c[1]-48*k*s^2-48*k*v*w)*U(xi)+(1/3)*(72*beta*s*c[2]+72*v*c[2])*U(xi)^3 = 0))*denom(lhs((24*alpha*s*c[1]+v*c[1])*(diff(diff(diff(diff(U(xi), xi), xi), xi), xi))+(-240*alpha*k^2*s*c[1]-6*k^2*v*c[1]+4*k^2*w*c[1])*(diff(diff(U(xi), xi), xi))+(120*alpha*k^4*s*c[1]+k^4*v*c[1]-4*k^4*w*c[1]-48*k*s^2-48*k*v*w)*U(xi)+(1/3)*(72*beta*s*c[2]+72*v*c[2])*U(xi)^3 = 0))

120*U(xi)*alpha*k^4*s*c[1]+U(xi)*k^4*v*c[1]-4*U(xi)*k^4*w*c[1]-240*(diff(diff(U(xi), xi), xi))*alpha*k^2*s*c[1]+24*U(xi)^3*beta*s*c[2]-6*(diff(diff(U(xi), xi), xi))*k^2*v*c[1]+4*(diff(diff(U(xi), xi), xi))*k^2*w*c[1]+24*U(xi)^3*v*c[2]+24*(diff(diff(diff(diff(U(xi), xi), xi), xi), xi))*alpha*s*c[1]-48*U(xi)*k*s^2-48*U(xi)*k*v*w+(diff(diff(diff(diff(U(xi), xi), xi), xi), xi))*v*c[1] = 0

 (13)
> 

RR := collect(%, {U(xi), diff(U(xi), xi), diff(U(xi), `$`(xi, 3)), diff(diff(U(xi), xi), xi), diff(diff(diff(diff(U(xi), xi), xi), xi), xi), diff(diff(diff(diff(diff(U(xi), xi), xi), xi), xi), xi)})

(24*beta*s*c[2]+24*v*c[2])*U(xi)^3+(120*alpha*k^4*s*c[1]+k^4*v*c[1]-4*k^4*w*c[1]-48*k*s^2-48*k*v*w)*U(xi)+(-240*alpha*k^2*s*c[1]-6*k^2*v*c[1]+4*k^2*w*c[1])*(diff(diff(U(xi), xi), xi))+(24*alpha*s*c[1]+v*c[1])*(diff(diff(diff(diff(U(xi), xi), xi), xi), xi)) = 0

 (14)
> 

IM := 24*U(xi)*k^2*s^2-24*U(xi)*k^2*w^2-24*U(xi)*alpha*k^5*s*c[1]+240*(diff(diff(U(xi), xi), xi))*alpha*k^3*s*c[1]-24*U(xi)^3*beta*k*s*c[2]-120*(diff(diff(diff(diff(U(xi), xi), xi), xi), xi))*alpha*k*s*c[1]+U(xi)*k^5*w*c[1]+4*(diff(diff(U(xi), xi), xi))*k^3*v*c[1]-6*(diff(diff(U(xi), xi), xi))*k^3*w*c[1]+24*U(xi)^3*k*w*c[2]-4*(diff(diff(diff(diff(U(xi), xi), xi), xi), xi))*k*v*c[1]+(diff(diff(diff(diff(U(xi), xi), xi), xi), xi))*k*w*c[1]-24*(diff(diff(U(xi), xi), xi))*s^2+24*(diff(diff(U(xi), xi), xi))*v^2 = 0
> 

collect(IM, {U(xi), diff(U(xi), xi), diff(U(xi), `$`(xi, 3)), diff(diff(U(xi), xi), xi), diff(diff(diff(diff(U(xi), xi), xi), xi), xi), diff(diff(diff(diff(diff(U(xi), xi), xi), xi), xi), xi)})
> 

P := %

(-24*beta*k*s*c[2]+24*k*w*c[2])*U(xi)^3+(-24*alpha*k^5*s*c[1]+k^5*w*c[1]+24*k^2*s^2-24*k^2*w^2)*U(xi)+(240*alpha*k^3*s*c[1]+4*k^3*v*c[1]-6*k^3*w*c[1]-24*s^2+24*v^2)*(diff(diff(U(xi), xi), xi))+(-120*alpha*k*s*c[1]-4*k*v*c[1]+k*w*c[1])*(diff(diff(diff(diff(U(xi), xi), xi), xi), xi)) = 0

 (15)
> 

NULL
> 

NULL
> 

C1 := v = solve(24*beta*s*c[2]+24*v*c[2] = 0, v)

v = -beta*s

 (16)
> 

C2 := w = solve(120*alpha*k^4*s*c[1]+k^4*v*c[1]-4*k^4*w*c[1]-48*k*s^2-48*k*v*w = 0, w)

w = (1/4)*(120*alpha*k^3*s*c[1]+k^3*v*c[1]-48*s^2)/(k^3*c[1]+12*v)

 (17)
> 

C3 := alpha = solve(-240*alpha*k^2*s*c[1]-6*k^2*v*c[1]+4*k^2*w*c[1] = 0, alpha)

alpha = -(1/120)*(3*v-2*w)/s

 (18)
> 

ode1 := subs({C1, C2, C3}, P)

(-24*beta*k*s*c[2]+6*k*(120*alpha*k^3*s*c[1]+k^3*v*c[1]-48*s^2)*c[2]/(k^3*c[1]+12*v))*U(xi)^3+((1/5)*(3*v-2*w)*k^5*c[1]+(1/4)*k^5*(120*alpha*k^3*s*c[1]+k^3*v*c[1]-48*s^2)*c[1]/(k^3*c[1]+12*v)+24*k^2*s^2-(3/2)*k^2*(120*alpha*k^3*s*c[1]+k^3*v*c[1]-48*s^2)^2/(k^3*c[1]+12*v)^2)*U(xi)+(-2*(3*v-2*w)*k^3*c[1]-4*k^3*beta*s*c[1]-(3/2)*k^3*(120*alpha*k^3*s*c[1]+k^3*v*c[1]-48*s^2)*c[1]/(k^3*c[1]+12*v)-24*s^2+24*beta^2*s^2)*(diff(diff(U(xi), xi), xi))+((3*v-2*w)*k*c[1]+4*k*beta*s*c[1]+(1/4)*k*(120*alpha*k^3*s*c[1]+k^3*v*c[1]-48*s^2)*c[1]/(k^3*c[1]+12*v))*(diff(diff(diff(diff(U(xi), xi), xi), xi), xi)) = 0

 (19)

Download F-condition_and_replacing.mw

how do I use dsolve() to solve a ordinary diffe...

Asked by: Dkunb 70
ode dsolve numeric
May 08 2025
1  13

I am not sure how to use dsolve for my problem.
CQ_v1.mw

Substitution of parts of a PDE...

Asked by: salim-barzani 1410
multiplication syntax 2dmath
May 07 2025
0  2

I'm trying to extract the real and imaginary parts of a given PDE. However, during the substitution step, something unexpected occurs. Specifically, my replacement does not yield the expected result, and an extra term appears: D(k)(t*w + x) in the expression P11. I'm unsure why this term arises and would appreciate any insight into what might be going wrong during the substitution process.

> 

restart
> 

with(PDEtools)
> 

with(LinearAlgebra)
> 

NULL
> 

with(SolveTools)
> 

undeclare(prime)

`There is no more prime differentiation variable; all derivatives will be displayed as indexed functions`

 (1)
> 

declare(u(x, t)); declare(U(xi)); declare(V(xi))

u(x, t)*`will now be displayed as`*u

  

U(xi)*`will now be displayed as`*U

  

V(xi)*`will now be displayed as`*V

 (2)
> 

pde := I*(diff(u(x, t), `$`(t, 2))-s^2*(diff(u(x, t), `$`(x, 2))))+(1/24)*c[1]*(diff(u(x, t), t, `$`(x, 4)))-alpha*s*c[1]*(diff(u(x, t), `$`(x, 5)))+diff(c[2]*u(x, t)*U(-t*v+x)^2+c[3]*u(x, t)*U(-t*v+x)^4+c[4]*u(x, t)*(diff(U(-t*v+x)^2, `$`(x, 2))), t)-beta*s*(diff(u(x, t), `$`(x, 5)))+diff(c[2]*u(x, t)*U(-t*v+x)^2+c[3]*u(x, t)*U(-t*v+x)^4+c[4]*u(x, t)*(diff(U(-t*v+x)^2, `$`(x, 2))), x)

I*(diff(diff(u(x, t), t), t)-s^2*(diff(diff(u(x, t), x), x)))+(1/24)*c[1]*(diff(diff(diff(diff(diff(u(x, t), t), x), x), x), x))-alpha*s*c[1]*(diff(diff(diff(diff(diff(u(x, t), x), x), x), x), x))+c[2]*(diff(u(x, t), t))*U(-t*v+x)^2-2*c[2]*u(x, t)*U(-t*v+x)*(D(U))(-t*v+x)*v+c[3]*(diff(u(x, t), t))*U(-t*v+x)^4-4*c[3]*u(x, t)*U(-t*v+x)^3*(D(U))(-t*v+x)*v+c[4]*(diff(u(x, t), t))*(2*(D(U))(-t*v+x)^2+2*U(-t*v+x)*((D@@2)(U))(-t*v+x))+c[4]*u(x, t)*(-6*(D(U))(-t*v+x)*((D@@2)(U))(-t*v+x)*v-2*U(-t*v+x)*((D@@3)(U))(-t*v+x)*v)-beta*s*(diff(diff(diff(diff(diff(u(x, t), x), x), x), x), x))+c[2]*(diff(u(x, t), x))*U(-t*v+x)^2+2*c[2]*u(x, t)*U(-t*v+x)*(D(U))(-t*v+x)+c[3]*(diff(u(x, t), x))*U(-t*v+x)^4+4*c[3]*u(x, t)*U(-t*v+x)^3*(D(U))(-t*v+x)+c[4]*(diff(u(x, t), x))*(2*(D(U))(-t*v+x)^2+2*U(-t*v+x)*((D@@2)(U))(-t*v+x))+c[4]*u(x, t)*(6*(D(U))(-t*v+x)*((D@@2)(U))(-t*v+x)+2*U(-t*v+x)*((D@@3)(U))(-t*v+x))

 (3)
> 

``
> 

G1 := U(-t*v+x) = U(xi); G2 := (D(U))(-t*v+x) = diff(U(xi), xi); G3 := ((D@@2)(U))(-t*v+x) = diff(U(xi), `$`(xi, 2)); G4 := ((D@@3)(U))(-t*v+x) = diff(U(xi), `$`(xi, 3)); G5 := ((D@@4)(U))(-t*v+x) = diff(U(xi), `$`(xi, 4)); G6 := ((D@@5)(U))(-t*v+x) = diff(U(xi), `$`(xi, 5))

U(-t*v+x) = U(xi)

  

(D(U))(-t*v+x) = diff(U(xi), xi)

  

((D@@2)(U))(-t*v+x) = diff(diff(U(xi), xi), xi)

  

((D@@3)(U))(-t*v+x) = diff(diff(diff(U(xi), xi), xi), xi)

  

((D@@4)(U))(-t*v+x) = diff(diff(diff(diff(U(xi), xi), xi), xi), xi)

  

((D@@5)(U))(-t*v+x) = diff(diff(diff(diff(diff(U(xi), xi), xi), xi), xi), xi)

 (4)
> 

NULL
> 

T := xi = -t*v+x; T1 := u(x, t) = U(-t*v+x)*exp(I*k(t*w+x))

xi = -t*v+x

  

u(x, t) = U(-t*v+x)*exp(I*k(t*w+x))

 (5)
> 

P1 := I*(diff(u(x, t), `$`(t, 2))-s^2*(diff(u(x, t), `$`(x, 2))))+(1/24)*c[1]*(diff(u(x, t), t, `$`(x, 4)))-alpha*s*c[1]*(diff(u(x, t), `$`(x, 5)))+diff(c[2]*u(x, t)*U(-t*v+x)^2+c[3]*u(x, t)*U(-t*v+x)^4+c[4]*u(x, t)*(diff(U(-t*v+x)^2, `$`(x, 2))), t)-beta*s*(diff(u(x, t), `$`(x, 5)))+diff(c[2]*u(x, t)*U(-t*v+x)^2+c[3]*u(x, t)*U(-t*v+x)^4+c[4]*u(x, t)*(diff(U(-t*v+x)^2, `$`(x, 2))), x)

I*(diff(diff(u(x, t), t), t)-s^2*(diff(diff(u(x, t), x), x)))+(1/24)*c[1]*(diff(diff(diff(diff(diff(u(x, t), t), x), x), x), x))-alpha*s*c[1]*(diff(diff(diff(diff(diff(u(x, t), x), x), x), x), x))+c[2]*(diff(u(x, t), t))*U(-t*v+x)^2-2*c[2]*u(x, t)*U(-t*v+x)*(D(U))(-t*v+x)*v+c[3]*(diff(u(x, t), t))*U(-t*v+x)^4-4*c[3]*u(x, t)*U(-t*v+x)^3*(D(U))(-t*v+x)*v+c[4]*(diff(u(x, t), t))*(2*(D(U))(-t*v+x)^2+2*U(-t*v+x)*((D@@2)(U))(-t*v+x))+c[4]*u(x, t)*(-6*(D(U))(-t*v+x)*((D@@2)(U))(-t*v+x)*v-2*U(-t*v+x)*((D@@3)(U))(-t*v+x)*v)-beta*s*(diff(diff(diff(diff(diff(u(x, t), x), x), x), x), x))+c[2]*(diff(u(x, t), x))*U(-t*v+x)^2+2*c[2]*u(x, t)*U(-t*v+x)*(D(U))(-t*v+x)+c[3]*(diff(u(x, t), x))*U(-t*v+x)^4+4*c[3]*u(x, t)*U(-t*v+x)^3*(D(U))(-t*v+x)+c[4]*(diff(u(x, t), x))*(2*(D(U))(-t*v+x)^2+2*U(-t*v+x)*((D@@2)(U))(-t*v+x))+c[4]*u(x, t)*(6*(D(U))(-t*v+x)*((D@@2)(U))(-t*v+x)+2*U(-t*v+x)*((D@@3)(U))(-t*v+x))

 (6)
> 

P11 := eval(P1, {T, T1})

I*(((D@@2)(U))(-t*v+x)*v^2*exp(I*k(t*w+x))-(2*I)*(D(U))(-t*v+x)*v*(D(k))(t*w+x)*w*exp(I*k(t*w+x))+I*U(-t*v+x)*((D@@2)(k))(t*w+x)*w^2*exp(I*k(t*w+x))-U(-t*v+x)*(D(k))(t*w+x)^2*w^2*exp(I*k(t*w+x))-s^2*(((D@@2)(U))(-t*v+x)*exp(I*k(t*w+x))+(2*I)*(D(U))(-t*v+x)*(D(k))(t*w+x)*exp(I*k(t*w+x))+I*U(-t*v+x)*((D@@2)(k))(t*w+x)*exp(I*k(t*w+x))-U(-t*v+x)*(D(k))(t*w+x)^2*exp(I*k(t*w+x))))+(1/24)*c[1]*(6*((D@@3)(U))(-t*v+x)*v*(D(k))(t*w+x)^2*exp(I*k(t*w+x))-4*((D@@3)(U))(-t*v+x)*(D(k))(t*w+x)^2*w*exp(I*k(t*w+x))+4*(D(U))(-t*v+x)*(D(k))(t*w+x)^4*w*exp(I*k(t*w+x))-(D(U))(-t*v+x)*v*(D(k))(t*w+x)^4*exp(I*k(t*w+x))+I*U(-t*v+x)*(D(k))(t*w+x)^5*w*exp(I*k(t*w+x))-(24*I)*(D(U))(-t*v+x)*(D(k))(t*w+x)^2*w*exp(I*k(t*w+x))*((D@@2)(k))(t*w+x)-(10*I)*U(-t*v+x)*((D@@3)(k))(t*w+x)*w*(D(k))(t*w+x)^2*exp(I*k(t*w+x))-(15*I)*U(-t*v+x)*((D@@2)(k))(t*w+x)^2*w*(D(k))(t*w+x)*exp(I*k(t*w+x))+(6*I)*(D(U))(-t*v+x)*v*(D(k))(t*w+x)^2*exp(I*k(t*w+x))*((D@@2)(k))(t*w+x)+12*((D@@2)(U))(-t*v+x)*v*(D(k))(t*w+x)*exp(I*k(t*w+x))*((D@@2)(k))(t*w+x)-18*((D@@2)(U))(-t*v+x)*(D(k))(t*w+x)*w*exp(I*k(t*w+x))*((D@@2)(k))(t*w+x)+10*U(-t*v+x)*(D(k))(t*w+x)^3*w*exp(I*k(t*w+x))*((D@@2)(k))(t*w+x)+I*((D@@4)(U))(-t*v+x)*(D(k))(t*w+x)*w*exp(I*k(t*w+x))-16*(D(U))(-t*v+x)*((D@@3)(k))(t*w+x)*w*(D(k))(t*w+x)*exp(I*k(t*w+x))-12*(D(U))(-t*v+x)*((D@@2)(k))(t*w+x)^2*w*exp(I*k(t*w+x))-5*U(-t*v+x)*((D@@4)(k))(t*w+x)*w*(D(k))(t*w+x)*exp(I*k(t*w+x))-10*U(-t*v+x)*((D@@3)(k))(t*w+x)*w*((D@@2)(k))(t*w+x)*exp(I*k(t*w+x))+I*U(-t*v+x)*((D@@5)(k))(t*w+x)*w*exp(I*k(t*w+x))-I*(D(U))(-t*v+x)*v*((D@@4)(k))(t*w+x)*exp(I*k(t*w+x))+3*(D(U))(-t*v+x)*v*((D@@2)(k))(t*w+x)^2*exp(I*k(t*w+x))+(4*I)*((D@@3)(U))(-t*v+x)*((D@@2)(k))(t*w+x)*w*exp(I*k(t*w+x))-(6*I)*((D@@2)(U))(-t*v+x)*(D(k))(t*w+x)^3*w*exp(I*k(t*w+x))-(6*I)*((D@@3)(U))(-t*v+x)*v*((D@@2)(k))(t*w+x)*exp(I*k(t*w+x))-(4*I)*((D@@2)(U))(-t*v+x)*v*((D@@3)(k))(t*w+x)*exp(I*k(t*w+x))+(6*I)*((D@@2)(U))(-t*v+x)*((D@@3)(k))(t*w+x)*w*exp(I*k(t*w+x))+(4*I)*(D(U))(-t*v+x)*((D@@4)(k))(t*w+x)*w*exp(I*k(t*w+x))+(4*I)*((D@@2)(U))(-t*v+x)*v*(D(k))(t*w+x)^3*exp(I*k(t*w+x))-(4*I)*((D@@4)(U))(-t*v+x)*v*(D(k))(t*w+x)*exp(I*k(t*w+x))+4*(D(U))(-t*v+x)*v*((D@@3)(k))(t*w+x)*(D(k))(t*w+x)*exp(I*k(t*w+x))-((D@@5)(U))(-t*v+x)*v*exp(I*k(t*w+x)))-alpha*s*c[1]*(I*U(-t*v+x)*((D@@5)(k))(t*w+x)*exp(I*k(t*w+x))+(10*I)*((D@@2)(U))(-t*v+x)*((D@@3)(k))(t*w+x)*exp(I*k(t*w+x))-(10*I)*((D@@2)(U))(-t*v+x)*(D(k))(t*w+x)^3*exp(I*k(t*w+x))-(30*I)*(D(U))(-t*v+x)*(D(k))(t*w+x)^2*exp(I*k(t*w+x))*((D@@2)(k))(t*w+x)+(5*I)*((D@@4)(U))(-t*v+x)*(D(k))(t*w+x)*exp(I*k(t*w+x))-10*U(-t*v+x)*((D@@3)(k))(t*w+x)*((D@@2)(k))(t*w+x)*exp(I*k(t*w+x))-15*(D(U))(-t*v+x)*((D@@2)(k))(t*w+x)^2*exp(I*k(t*w+x))+10*U(-t*v+x)*(D(k))(t*w+x)^3*exp(I*k(t*w+x))*((D@@2)(k))(t*w+x)+(5*I)*(D(U))(-t*v+x)*((D@@4)(k))(t*w+x)*exp(I*k(t*w+x))-5*U(-t*v+x)*((D@@4)(k))(t*w+x)*(D(k))(t*w+x)*exp(I*k(t*w+x))-20*(D(U))(-t*v+x)*((D@@3)(k))(t*w+x)*(D(k))(t*w+x)*exp(I*k(t*w+x))-30*((D@@2)(U))(-t*v+x)*(D(k))(t*w+x)*exp(I*k(t*w+x))*((D@@2)(k))(t*w+x)-(10*I)*U(-t*v+x)*((D@@3)(k))(t*w+x)*(D(k))(t*w+x)^2*exp(I*k(t*w+x))-(15*I)*U(-t*v+x)*((D@@2)(k))(t*w+x)^2*(D(k))(t*w+x)*exp(I*k(t*w+x))+I*U(-t*v+x)*(D(k))(t*w+x)^5*exp(I*k(t*w+x))+(10*I)*((D@@3)(U))(-t*v+x)*((D@@2)(k))(t*w+x)*exp(I*k(t*w+x))+((D@@5)(U))(-t*v+x)*exp(I*k(t*w+x))+5*(D(U))(-t*v+x)*(D(k))(t*w+x)^4*exp(I*k(t*w+x))-10*((D@@3)(U))(-t*v+x)*(D(k))(t*w+x)^2*exp(I*k(t*w+x)))+c[2]*(-(D(U))(-t*v+x)*v*exp(I*k(t*w+x))+I*U(-t*v+x)*(D(k))(t*w+x)*w*exp(I*k(t*w+x)))*U(-t*v+x)^2-2*c[2]*U(-t*v+x)^2*exp(I*k(t*w+x))*(D(U))(-t*v+x)*v+c[3]*(-(D(U))(-t*v+x)*v*exp(I*k(t*w+x))+I*U(-t*v+x)*(D(k))(t*w+x)*w*exp(I*k(t*w+x)))*U(-t*v+x)^4-4*c[3]*U(-t*v+x)^4*exp(I*k(t*w+x))*(D(U))(-t*v+x)*v+c[4]*(-(D(U))(-t*v+x)*v*exp(I*k(t*w+x))+I*U(-t*v+x)*(D(k))(t*w+x)*w*exp(I*k(t*w+x)))*(2*(D(U))(-t*v+x)^2+2*U(-t*v+x)*((D@@2)(U))(-t*v+x))+c[4]*U(-t*v+x)*exp(I*k(t*w+x))*(-6*(D(U))(-t*v+x)*((D@@2)(U))(-t*v+x)*v-2*U(-t*v+x)*((D@@3)(U))(-t*v+x)*v)-beta*s*(I*U(-t*v+x)*((D@@5)(k))(t*w+x)*exp(I*k(t*w+x))+(10*I)*((D@@2)(U))(-t*v+x)*((D@@3)(k))(t*w+x)*exp(I*k(t*w+x))-(10*I)*((D@@2)(U))(-t*v+x)*(D(k))(t*w+x)^3*exp(I*k(t*w+x))-(30*I)*(D(U))(-t*v+x)*(D(k))(t*w+x)^2*exp(I*k(t*w+x))*((D@@2)(k))(t*w+x)+(5*I)*((D@@4)(U))(-t*v+x)*(D(k))(t*w+x)*exp(I*k(t*w+x))-10*U(-t*v+x)*((D@@3)(k))(t*w+x)*((D@@2)(k))(t*w+x)*exp(I*k(t*w+x))-15*(D(U))(-t*v+x)*((D@@2)(k))(t*w+x)^2*exp(I*k(t*w+x))+10*U(-t*v+x)*(D(k))(t*w+x)^3*exp(I*k(t*w+x))*((D@@2)(k))(t*w+x)+(5*I)*(D(U))(-t*v+x)*((D@@4)(k))(t*w+x)*exp(I*k(t*w+x))-5*U(-t*v+x)*((D@@4)(k))(t*w+x)*(D(k))(t*w+x)*exp(I*k(t*w+x))-20*(D(U))(-t*v+x)*((D@@3)(k))(t*w+x)*(D(k))(t*w+x)*exp(I*k(t*w+x))-30*((D@@2)(U))(-t*v+x)*(D(k))(t*w+x)*exp(I*k(t*w+x))*((D@@2)(k))(t*w+x)-(10*I)*U(-t*v+x)*((D@@3)(k))(t*w+x)*(D(k))(t*w+x)^2*exp(I*k(t*w+x))-(15*I)*U(-t*v+x)*((D@@2)(k))(t*w+x)^2*(D(k))(t*w+x)*exp(I*k(t*w+x))+I*U(-t*v+x)*(D(k))(t*w+x)^5*exp(I*k(t*w+x))+(10*I)*((D@@3)(U))(-t*v+x)*((D@@2)(k))(t*w+x)*exp(I*k(t*w+x))+((D@@5)(U))(-t*v+x)*exp(I*k(t*w+x))+5*(D(U))(-t*v+x)*(D(k))(t*w+x)^4*exp(I*k(t*w+x))-10*((D@@3)(U))(-t*v+x)*(D(k))(t*w+x)^2*exp(I*k(t*w+x)))+c[2]*((D(U))(-t*v+x)*exp(I*k(t*w+x))+I*U(-t*v+x)*(D(k))(t*w+x)*exp(I*k(t*w+x)))*U(-t*v+x)^2+2*c[2]*U(-t*v+x)^2*exp(I*k(t*w+x))*(D(U))(-t*v+x)+c[3]*((D(U))(-t*v+x)*exp(I*k(t*w+x))+I*U(-t*v+x)*(D(k))(t*w+x)*exp(I*k(t*w+x)))*U(-t*v+x)^4+4*c[3]*U(-t*v+x)^4*exp(I*k(t*w+x))*(D(U))(-t*v+x)+c[4]*((D(U))(-t*v+x)*exp(I*k(t*w+x))+I*U(-t*v+x)*(D(k))(t*w+x)*exp(I*k(t*w+x)))*(2*(D(U))(-t*v+x)^2+2*U(-t*v+x)*((D@@2)(U))(-t*v+x))+c[4]*U(-t*v+x)*exp(I*k(t*w+x))*(6*(D(U))(-t*v+x)*((D@@2)(U))(-t*v+x)+2*U(-t*v+x)*((D@@3)(U))(-t*v+x))

 (7)
> 

P111 := subs({G1, G2, G3, G4, G5, G6}, P11)NULL

I*((diff(diff(U(xi), xi), xi))*v^2*exp(I*k(t*w+x))-(2*I)*(diff(U(xi), xi))*v*(D(k))(t*w+x)*w*exp(I*k(t*w+x))+I*U(xi)*((D@@2)(k))(t*w+x)*w^2*exp(I*k(t*w+x))-U(xi)*(D(k))(t*w+x)^2*w^2*exp(I*k(t*w+x))-s^2*((diff(diff(U(xi), xi), xi))*exp(I*k(t*w+x))+(2*I)*(diff(U(xi), xi))*(D(k))(t*w+x)*exp(I*k(t*w+x))+I*U(xi)*((D@@2)(k))(t*w+x)*exp(I*k(t*w+x))-U(xi)*(D(k))(t*w+x)^2*exp(I*k(t*w+x))))+(1/24)*c[1]*(6*(diff(diff(diff(U(xi), xi), xi), xi))*v*(D(k))(t*w+x)^2*exp(I*k(t*w+x))-4*(diff(diff(diff(U(xi), xi), xi), xi))*(D(k))(t*w+x)^2*w*exp(I*k(t*w+x))+4*(diff(U(xi), xi))*(D(k))(t*w+x)^4*w*exp(I*k(t*w+x))-(diff(U(xi), xi))*v*(D(k))(t*w+x)^4*exp(I*k(t*w+x))-12*(diff(U(xi), xi))*((D@@2)(k))(t*w+x)^2*w*exp(I*k(t*w+x))+3*(diff(U(xi), xi))*v*((D@@2)(k))(t*w+x)^2*exp(I*k(t*w+x))+I*U(xi)*(D(k))(t*w+x)^5*w*exp(I*k(t*w+x))+12*(diff(diff(U(xi), xi), xi))*v*(D(k))(t*w+x)*exp(I*k(t*w+x))*((D@@2)(k))(t*w+x)-18*(diff(diff(U(xi), xi), xi))*(D(k))(t*w+x)*w*exp(I*k(t*w+x))*((D@@2)(k))(t*w+x)+10*U(xi)*(D(k))(t*w+x)^3*w*exp(I*k(t*w+x))*((D@@2)(k))(t*w+x)+I*(diff(diff(diff(diff(U(xi), xi), xi), xi), xi))*(D(k))(t*w+x)*w*exp(I*k(t*w+x))-16*(diff(U(xi), xi))*((D@@3)(k))(t*w+x)*w*(D(k))(t*w+x)*exp(I*k(t*w+x))-5*U(xi)*((D@@4)(k))(t*w+x)*w*(D(k))(t*w+x)*exp(I*k(t*w+x))-10*U(xi)*((D@@3)(k))(t*w+x)*w*((D@@2)(k))(t*w+x)*exp(I*k(t*w+x))+I*U(xi)*((D@@5)(k))(t*w+x)*w*exp(I*k(t*w+x))-I*(diff(U(xi), xi))*v*((D@@4)(k))(t*w+x)*exp(I*k(t*w+x))+(4*I)*(diff(diff(diff(U(xi), xi), xi), xi))*((D@@2)(k))(t*w+x)*w*exp(I*k(t*w+x))-(6*I)*(diff(diff(U(xi), xi), xi))*(D(k))(t*w+x)^3*w*exp(I*k(t*w+x))-(6*I)*(diff(diff(diff(U(xi), xi), xi), xi))*v*((D@@2)(k))(t*w+x)*exp(I*k(t*w+x))-(4*I)*(diff(diff(U(xi), xi), xi))*v*((D@@3)(k))(t*w+x)*exp(I*k(t*w+x))+(6*I)*(diff(diff(U(xi), xi), xi))*((D@@3)(k))(t*w+x)*w*exp(I*k(t*w+x))+(4*I)*(diff(U(xi), xi))*((D@@4)(k))(t*w+x)*w*exp(I*k(t*w+x))+(4*I)*(diff(diff(U(xi), xi), xi))*v*(D(k))(t*w+x)^3*exp(I*k(t*w+x))-(4*I)*(diff(diff(diff(diff(U(xi), xi), xi), xi), xi))*v*(D(k))(t*w+x)*exp(I*k(t*w+x))+4*(diff(U(xi), xi))*v*((D@@3)(k))(t*w+x)*(D(k))(t*w+x)*exp(I*k(t*w+x))-(diff(diff(diff(diff(diff(U(xi), xi), xi), xi), xi), xi))*v*exp(I*k(t*w+x))-(10*I)*U(xi)*((D@@3)(k))(t*w+x)*w*(D(k))(t*w+x)^2*exp(I*k(t*w+x))-(15*I)*U(xi)*((D@@2)(k))(t*w+x)^2*w*(D(k))(t*w+x)*exp(I*k(t*w+x))+(6*I)*(diff(U(xi), xi))*v*(D(k))(t*w+x)^2*exp(I*k(t*w+x))*((D@@2)(k))(t*w+x)-(24*I)*(diff(U(xi), xi))*(D(k))(t*w+x)^2*w*exp(I*k(t*w+x))*((D@@2)(k))(t*w+x))-alpha*s*c[1]*(-(30*I)*(diff(U(xi), xi))*(D(k))(t*w+x)^2*exp(I*k(t*w+x))*((D@@2)(k))(t*w+x)+(5*I)*(diff(U(xi), xi))*((D@@4)(k))(t*w+x)*exp(I*k(t*w+x))+I*U(xi)*(D(k))(t*w+x)^5*exp(I*k(t*w+x))+(10*I)*(diff(diff(diff(U(xi), xi), xi), xi))*((D@@2)(k))(t*w+x)*exp(I*k(t*w+x))+I*U(xi)*((D@@5)(k))(t*w+x)*exp(I*k(t*w+x))-10*U(xi)*((D@@3)(k))(t*w+x)*((D@@2)(k))(t*w+x)*exp(I*k(t*w+x))-15*(diff(U(xi), xi))*((D@@2)(k))(t*w+x)^2*exp(I*k(t*w+x))+10*U(xi)*(D(k))(t*w+x)^3*exp(I*k(t*w+x))*((D@@2)(k))(t*w+x)+(10*I)*(diff(diff(U(xi), xi), xi))*((D@@3)(k))(t*w+x)*exp(I*k(t*w+x))-5*U(xi)*((D@@4)(k))(t*w+x)*(D(k))(t*w+x)*exp(I*k(t*w+x))-20*(diff(U(xi), xi))*((D@@3)(k))(t*w+x)*(D(k))(t*w+x)*exp(I*k(t*w+x))-30*(diff(diff(U(xi), xi), xi))*(D(k))(t*w+x)*exp(I*k(t*w+x))*((D@@2)(k))(t*w+x)-(10*I)*(diff(diff(U(xi), xi), xi))*(D(k))(t*w+x)^3*exp(I*k(t*w+x))+(5*I)*(diff(diff(diff(diff(U(xi), xi), xi), xi), xi))*(D(k))(t*w+x)*exp(I*k(t*w+x))-(10*I)*U(xi)*((D@@3)(k))(t*w+x)*(D(k))(t*w+x)^2*exp(I*k(t*w+x))-(15*I)*U(xi)*((D@@2)(k))(t*w+x)^2*(D(k))(t*w+x)*exp(I*k(t*w+x))+(diff(diff(diff(diff(diff(U(xi), xi), xi), xi), xi), xi))*exp(I*k(t*w+x))+5*(diff(U(xi), xi))*(D(k))(t*w+x)^4*exp(I*k(t*w+x))-10*(diff(diff(diff(U(xi), xi), xi), xi))*(D(k))(t*w+x)^2*exp(I*k(t*w+x)))+c[2]*(-(diff(U(xi), xi))*v*exp(I*k(t*w+x))+I*U(xi)*(D(k))(t*w+x)*w*exp(I*k(t*w+x)))*U(xi)^2-2*exp(I*k(t*w+x))*(diff(U(xi), xi))*U(xi)^2*v*c[2]+c[3]*(-(diff(U(xi), xi))*v*exp(I*k(t*w+x))+I*U(xi)*(D(k))(t*w+x)*w*exp(I*k(t*w+x)))*U(xi)^4-4*exp(I*k(t*w+x))*(diff(U(xi), xi))*U(xi)^4*v*c[3]+c[4]*(-(diff(U(xi), xi))*v*exp(I*k(t*w+x))+I*U(xi)*(D(k))(t*w+x)*w*exp(I*k(t*w+x)))*(2*(diff(U(xi), xi))^2+2*U(xi)*(diff(diff(U(xi), xi), xi)))+c[4]*U(xi)*exp(I*k(t*w+x))*(-6*(diff(U(xi), xi))*(diff(diff(U(xi), xi), xi))*v-2*U(xi)*(diff(diff(diff(U(xi), xi), xi), xi))*v)-beta*s*(-(30*I)*(diff(U(xi), xi))*(D(k))(t*w+x)^2*exp(I*k(t*w+x))*((D@@2)(k))(t*w+x)+(5*I)*(diff(U(xi), xi))*((D@@4)(k))(t*w+x)*exp(I*k(t*w+x))+I*U(xi)*(D(k))(t*w+x)^5*exp(I*k(t*w+x))+(10*I)*(diff(diff(diff(U(xi), xi), xi), xi))*((D@@2)(k))(t*w+x)*exp(I*k(t*w+x))+I*U(xi)*((D@@5)(k))(t*w+x)*exp(I*k(t*w+x))-10*U(xi)*((D@@3)(k))(t*w+x)*((D@@2)(k))(t*w+x)*exp(I*k(t*w+x))-15*(diff(U(xi), xi))*((D@@2)(k))(t*w+x)^2*exp(I*k(t*w+x))+10*U(xi)*(D(k))(t*w+x)^3*exp(I*k(t*w+x))*((D@@2)(k))(t*w+x)+(10*I)*(diff(diff(U(xi), xi), xi))*((D@@3)(k))(t*w+x)*exp(I*k(t*w+x))-5*U(xi)*((D@@4)(k))(t*w+x)*(D(k))(t*w+x)*exp(I*k(t*w+x))-20*(diff(U(xi), xi))*((D@@3)(k))(t*w+x)*(D(k))(t*w+x)*exp(I*k(t*w+x))-30*(diff(diff(U(xi), xi), xi))*(D(k))(t*w+x)*exp(I*k(t*w+x))*((D@@2)(k))(t*w+x)-(10*I)*(diff(diff(U(xi), xi), xi))*(D(k))(t*w+x)^3*exp(I*k(t*w+x))+(5*I)*(diff(diff(diff(diff(U(xi), xi), xi), xi), xi))*(D(k))(t*w+x)*exp(I*k(t*w+x))-(10*I)*U(xi)*((D@@3)(k))(t*w+x)*(D(k))(t*w+x)^2*exp(I*k(t*w+x))-(15*I)*U(xi)*((D@@2)(k))(t*w+x)^2*(D(k))(t*w+x)*exp(I*k(t*w+x))+(diff(diff(diff(diff(diff(U(xi), xi), xi), xi), xi), xi))*exp(I*k(t*w+x))+5*(diff(U(xi), xi))*(D(k))(t*w+x)^4*exp(I*k(t*w+x))-10*(diff(diff(diff(U(xi), xi), xi), xi))*(D(k))(t*w+x)^2*exp(I*k(t*w+x)))+c[2]*((diff(U(xi), xi))*exp(I*k(t*w+x))+I*U(xi)*(D(k))(t*w+x)*exp(I*k(t*w+x)))*U(xi)^2+2*exp(I*k(t*w+x))*(diff(U(xi), xi))*U(xi)^2*c[2]+c[3]*((diff(U(xi), xi))*exp(I*k(t*w+x))+I*U(xi)*(D(k))(t*w+x)*exp(I*k(t*w+x)))*U(xi)^4+4*exp(I*k(t*w+x))*(diff(U(xi), xi))*U(xi)^4*c[3]+c[4]*((diff(U(xi), xi))*exp(I*k(t*w+x))+I*U(xi)*(D(k))(t*w+x)*exp(I*k(t*w+x)))*(2*(diff(U(xi), xi))^2+2*U(xi)*(diff(diff(U(xi), xi), xi)))+c[4]*U(xi)*exp(I*k(t*w+x))*(6*(diff(U(xi), xi))*(diff(diff(U(xi), xi), xi))+2*U(xi)*(diff(diff(diff(U(xi), xi), xi), xi)))

 (8)
> 

``
> 

pde1 := P111 = 0

I*((diff(diff(U(xi), xi), xi))*v^2*exp(I*k(t*w+x))-(2*I)*(diff(U(xi), xi))*v*(D(k))(t*w+x)*w*exp(I*k(t*w+x))+I*U(xi)*((D@@2)(k))(t*w+x)*w^2*exp(I*k(t*w+x))-U(xi)*(D(k))(t*w+x)^2*w^2*exp(I*k(t*w+x))-s^2*((diff(diff(U(xi), xi), xi))*exp(I*k(t*w+x))+(2*I)*(diff(U(xi), xi))*(D(k))(t*w+x)*exp(I*k(t*w+x))+I*U(xi)*((D@@2)(k))(t*w+x)*exp(I*k(t*w+x))-U(xi)*(D(k))(t*w+x)^2*exp(I*k(t*w+x))))+(1/24)*c[1]*(6*(diff(diff(diff(U(xi), xi), xi), xi))*v*(D(k))(t*w+x)^2*exp(I*k(t*w+x))-4*(diff(diff(diff(U(xi), xi), xi), xi))*(D(k))(t*w+x)^2*w*exp(I*k(t*w+x))+4*(diff(U(xi), xi))*(D(k))(t*w+x)^4*w*exp(I*k(t*w+x))-(diff(U(xi), xi))*v*(D(k))(t*w+x)^4*exp(I*k(t*w+x))-12*(diff(U(xi), xi))*((D@@2)(k))(t*w+x)^2*w*exp(I*k(t*w+x))+3*(diff(U(xi), xi))*v*((D@@2)(k))(t*w+x)^2*exp(I*k(t*w+x))+I*U(xi)*(D(k))(t*w+x)^5*w*exp(I*k(t*w+x))+12*(diff(diff(U(xi), xi), xi))*v*(D(k))(t*w+x)*exp(I*k(t*w+x))*((D@@2)(k))(t*w+x)-18*(diff(diff(U(xi), xi), xi))*(D(k))(t*w+x)*w*exp(I*k(t*w+x))*((D@@2)(k))(t*w+x)+10*U(xi)*(D(k))(t*w+x)^3*w*exp(I*k(t*w+x))*((D@@2)(k))(t*w+x)+I*(diff(diff(diff(diff(U(xi), xi), xi), xi), xi))*(D(k))(t*w+x)*w*exp(I*k(t*w+x))-16*(diff(U(xi), xi))*((D@@3)(k))(t*w+x)*w*(D(k))(t*w+x)*exp(I*k(t*w+x))-5*U(xi)*((D@@4)(k))(t*w+x)*w*(D(k))(t*w+x)*exp(I*k(t*w+x))-10*U(xi)*((D@@3)(k))(t*w+x)*w*((D@@2)(k))(t*w+x)*exp(I*k(t*w+x))+I*U(xi)*((D@@5)(k))(t*w+x)*w*exp(I*k(t*w+x))-I*(diff(U(xi), xi))*v*((D@@4)(k))(t*w+x)*exp(I*k(t*w+x))+(4*I)*(diff(diff(diff(U(xi), xi), xi), xi))*((D@@2)(k))(t*w+x)*w*exp(I*k(t*w+x))-(6*I)*(diff(diff(U(xi), xi), xi))*(D(k))(t*w+x)^3*w*exp(I*k(t*w+x))-(6*I)*(diff(diff(diff(U(xi), xi), xi), xi))*v*((D@@2)(k))(t*w+x)*exp(I*k(t*w+x))-(4*I)*(diff(diff(U(xi), xi), xi))*v*((D@@3)(k))(t*w+x)*exp(I*k(t*w+x))+(6*I)*(diff(diff(U(xi), xi), xi))*((D@@3)(k))(t*w+x)*w*exp(I*k(t*w+x))+(4*I)*(diff(U(xi), xi))*((D@@4)(k))(t*w+x)*w*exp(I*k(t*w+x))+(4*I)*(diff(diff(U(xi), xi), xi))*v*(D(k))(t*w+x)^3*exp(I*k(t*w+x))-(4*I)*(diff(diff(diff(diff(U(xi), xi), xi), xi), xi))*v*(D(k))(t*w+x)*exp(I*k(t*w+x))+4*(diff(U(xi), xi))*v*((D@@3)(k))(t*w+x)*(D(k))(t*w+x)*exp(I*k(t*w+x))-(diff(diff(diff(diff(diff(U(xi), xi), xi), xi), xi), xi))*v*exp(I*k(t*w+x))-(10*I)*U(xi)*((D@@3)(k))(t*w+x)*w*(D(k))(t*w+x)^2*exp(I*k(t*w+x))-(15*I)*U(xi)*((D@@2)(k))(t*w+x)^2*w*(D(k))(t*w+x)*exp(I*k(t*w+x))+(6*I)*(diff(U(xi), xi))*v*(D(k))(t*w+x)^2*exp(I*k(t*w+x))*((D@@2)(k))(t*w+x)-(24*I)*(diff(U(xi), xi))*(D(k))(t*w+x)^2*w*exp(I*k(t*w+x))*((D@@2)(k))(t*w+x))-alpha*s*c[1]*(-(30*I)*(diff(U(xi), xi))*(D(k))(t*w+x)^2*exp(I*k(t*w+x))*((D@@2)(k))(t*w+x)+(5*I)*(diff(U(xi), xi))*((D@@4)(k))(t*w+x)*exp(I*k(t*w+x))+I*U(xi)*(D(k))(t*w+x)^5*exp(I*k(t*w+x))+(10*I)*(diff(diff(diff(U(xi), xi), xi), xi))*((D@@2)(k))(t*w+x)*exp(I*k(t*w+x))+I*U(xi)*((D@@5)(k))(t*w+x)*exp(I*k(t*w+x))-10*U(xi)*((D@@3)(k))(t*w+x)*((D@@2)(k))(t*w+x)*exp(I*k(t*w+x))-15*(diff(U(xi), xi))*((D@@2)(k))(t*w+x)^2*exp(I*k(t*w+x))+10*U(xi)*(D(k))(t*w+x)^3*exp(I*k(t*w+x))*((D@@2)(k))(t*w+x)+(10*I)*(diff(diff(U(xi), xi), xi))*((D@@3)(k))(t*w+x)*exp(I*k(t*w+x))-5*U(xi)*((D@@4)(k))(t*w+x)*(D(k))(t*w+x)*exp(I*k(t*w+x))-20*(diff(U(xi), xi))*((D@@3)(k))(t*w+x)*(D(k))(t*w+x)*exp(I*k(t*w+x))-30*(diff(diff(U(xi), xi), xi))*(D(k))(t*w+x)*exp(I*k(t*w+x))*((D@@2)(k))(t*w+x)-(10*I)*(diff(diff(U(xi), xi), xi))*(D(k))(t*w+x)^3*exp(I*k(t*w+x))+(5*I)*(diff(diff(diff(diff(U(xi), xi), xi), xi), xi))*(D(k))(t*w+x)*exp(I*k(t*w+x))-(10*I)*U(xi)*((D@@3)(k))(t*w+x)*(D(k))(t*w+x)^2*exp(I*k(t*w+x))-(15*I)*U(xi)*((D@@2)(k))(t*w+x)^2*(D(k))(t*w+x)*exp(I*k(t*w+x))+(diff(diff(diff(diff(diff(U(xi), xi), xi), xi), xi), xi))*exp(I*k(t*w+x))+5*(diff(U(xi), xi))*(D(k))(t*w+x)^4*exp(I*k(t*w+x))-10*(diff(diff(diff(U(xi), xi), xi), xi))*(D(k))(t*w+x)^2*exp(I*k(t*w+x)))+c[2]*(-(diff(U(xi), xi))*v*exp(I*k(t*w+x))+I*U(xi)*(D(k))(t*w+x)*w*exp(I*k(t*w+x)))*U(xi)^2-2*exp(I*k(t*w+x))*(diff(U(xi), xi))*U(xi)^2*v*c[2]+c[3]*(-(diff(U(xi), xi))*v*exp(I*k(t*w+x))+I*U(xi)*(D(k))(t*w+x)*w*exp(I*k(t*w+x)))*U(xi)^4-4*exp(I*k(t*w+x))*(diff(U(xi), xi))*U(xi)^4*v*c[3]+c[4]*(-(diff(U(xi), xi))*v*exp(I*k(t*w+x))+I*U(xi)*(D(k))(t*w+x)*w*exp(I*k(t*w+x)))*(2*(diff(U(xi), xi))^2+2*U(xi)*(diff(diff(U(xi), xi), xi)))+c[4]*U(xi)*exp(I*k(t*w+x))*(-6*(diff(U(xi), xi))*(diff(diff(U(xi), xi), xi))*v-2*U(xi)*(diff(diff(diff(U(xi), xi), xi), xi))*v)-beta*s*(-(30*I)*(diff(U(xi), xi))*(D(k))(t*w+x)^2*exp(I*k(t*w+x))*((D@@2)(k))(t*w+x)+(5*I)*(diff(U(xi), xi))*((D@@4)(k))(t*w+x)*exp(I*k(t*w+x))+I*U(xi)*(D(k))(t*w+x)^5*exp(I*k(t*w+x))+(10*I)*(diff(diff(diff(U(xi), xi), xi), xi))*((D@@2)(k))(t*w+x)*exp(I*k(t*w+x))+I*U(xi)*((D@@5)(k))(t*w+x)*exp(I*k(t*w+x))-10*U(xi)*((D@@3)(k))(t*w+x)*((D@@2)(k))(t*w+x)*exp(I*k(t*w+x))-15*(diff(U(xi), xi))*((D@@2)(k))(t*w+x)^2*exp(I*k(t*w+x))+10*U(xi)*(D(k))(t*w+x)^3*exp(I*k(t*w+x))*((D@@2)(k))(t*w+x)+(10*I)*(diff(diff(U(xi), xi), xi))*((D@@3)(k))(t*w+x)*exp(I*k(t*w+x))-5*U(xi)*((D@@4)(k))(t*w+x)*(D(k))(t*w+x)*exp(I*k(t*w+x))-20*(diff(U(xi), xi))*((D@@3)(k))(t*w+x)*(D(k))(t*w+x)*exp(I*k(t*w+x))-30*(diff(diff(U(xi), xi), xi))*(D(k))(t*w+x)*exp(I*k(t*w+x))*((D@@2)(k))(t*w+x)-(10*I)*(diff(diff(U(xi), xi), xi))*(D(k))(t*w+x)^3*exp(I*k(t*w+x))+(5*I)*(diff(diff(diff(diff(U(xi), xi), xi), xi), xi))*(D(k))(t*w+x)*exp(I*k(t*w+x))-(10*I)*U(xi)*((D@@3)(k))(t*w+x)*(D(k))(t*w+x)^2*exp(I*k(t*w+x))-(15*I)*U(xi)*((D@@2)(k))(t*w+x)^2*(D(k))(t*w+x)*exp(I*k(t*w+x))+(diff(diff(diff(diff(diff(U(xi), xi), xi), xi), xi), xi))*exp(I*k(t*w+x))+5*(diff(U(xi), xi))*(D(k))(t*w+x)^4*exp(I*k(t*w+x))-10*(diff(diff(diff(U(xi), xi), xi), xi))*(D(k))(t*w+x)^2*exp(I*k(t*w+x)))+c[2]*((diff(U(xi), xi))*exp(I*k(t*w+x))+I*U(xi)*(D(k))(t*w+x)*exp(I*k(t*w+x)))*U(xi)^2+2*exp(I*k(t*w+x))*(diff(U(xi), xi))*U(xi)^2*c[2]+c[3]*((diff(U(xi), xi))*exp(I*k(t*w+x))+I*U(xi)*(D(k))(t*w+x)*exp(I*k(t*w+x)))*U(xi)^4+4*exp(I*k(t*w+x))*(diff(U(xi), xi))*U(xi)^4*c[3]+c[4]*((diff(U(xi), xi))*exp(I*k(t*w+x))+I*U(xi)*(D(k))(t*w+x)*exp(I*k(t*w+x)))*(2*(diff(U(xi), xi))^2+2*U(xi)*(diff(diff(U(xi), xi), xi)))+c[4]*U(xi)*exp(I*k(t*w+x))*(6*(diff(U(xi), xi))*(diff(diff(U(xi), xi), xi))+2*U(xi)*(diff(diff(diff(U(xi), xi), xi), xi))) = 0

 (9)
> 

numer(lhs(I*((diff(diff(U(xi), xi), xi))*v^2*exp(I*k(t*w+x))-(2*I)*(diff(U(xi), xi))*v*(D(k))(t*w+x)*w*exp(I*k(t*w+x))+I*U(xi)*((D@@2)(k))(t*w+x)*w^2*exp(I*k(t*w+x))-U(xi)*(D(k))(t*w+x)^2*w^2*exp(I*k(t*w+x))-s^2*((diff(diff(U(xi), xi), xi))*exp(I*k(t*w+x))+(2*I)*(diff(U(xi), xi))*(D(k))(t*w+x)*exp(I*k(t*w+x))+I*U(xi)*((D@@2)(k))(t*w+x)*exp(I*k(t*w+x))-U(xi)*(D(k))(t*w+x)^2*exp(I*k(t*w+x))))+(1/24)*c[1]*(-(diff(diff(diff(diff(diff(U(xi), xi), xi), xi), xi), xi))*v*exp(I*k(t*w+x))+6*(diff(diff(diff(U(xi), xi), xi), xi))*v*(D(k))(t*w+x)^2*exp(I*k(t*w+x))-4*(diff(diff(diff(U(xi), xi), xi), xi))*(D(k))(t*w+x)^2*w*exp(I*k(t*w+x))+4*(diff(U(xi), xi))*(D(k))(t*w+x)^4*w*exp(I*k(t*w+x))-12*(diff(U(xi), xi))*((D@@2)(k))(t*w+x)^2*w*exp(I*k(t*w+x))+3*(diff(U(xi), xi))*v*((D@@2)(k))(t*w+x)^2*exp(I*k(t*w+x))-(diff(U(xi), xi))*v*(D(k))(t*w+x)^4*exp(I*k(t*w+x))-10*U(xi)*((D@@3)(k))(t*w+x)*w*((D@@2)(k))(t*w+x)*exp(I*k(t*w+x))+4*(diff(U(xi), xi))*v*((D@@3)(k))(t*w+x)*(D(k))(t*w+x)*exp(I*k(t*w+x))-I*(diff(U(xi), xi))*v*((D@@4)(k))(t*w+x)*exp(I*k(t*w+x))-(6*I)*(diff(diff(U(xi), xi), xi))*(D(k))(t*w+x)^3*w*exp(I*k(t*w+x))-(6*I)*(diff(diff(diff(U(xi), xi), xi), xi))*v*((D@@2)(k))(t*w+x)*exp(I*k(t*w+x))-(4*I)*(diff(diff(U(xi), xi), xi))*v*((D@@3)(k))(t*w+x)*exp(I*k(t*w+x))-(4*I)*(diff(diff(diff(diff(U(xi), xi), xi), xi), xi))*v*(D(k))(t*w+x)*exp(I*k(t*w+x))+I*U(xi)*(D(k))(t*w+x)^5*w*exp(I*k(t*w+x))+I*(diff(diff(diff(diff(U(xi), xi), xi), xi), xi))*(D(k))(t*w+x)*w*exp(I*k(t*w+x))+I*U(xi)*((D@@5)(k))(t*w+x)*w*exp(I*k(t*w+x))+(4*I)*(diff(diff(diff(U(xi), xi), xi), xi))*((D@@2)(k))(t*w+x)*w*exp(I*k(t*w+x))+(6*I)*(diff(diff(U(xi), xi), xi))*((D@@3)(k))(t*w+x)*w*exp(I*k(t*w+x))+(4*I)*(diff(U(xi), xi))*((D@@4)(k))(t*w+x)*w*exp(I*k(t*w+x))+(4*I)*(diff(diff(U(xi), xi), xi))*v*(D(k))(t*w+x)^3*exp(I*k(t*w+x))+12*(diff(diff(U(xi), xi), xi))*v*(D(k))(t*w+x)*exp(I*k(t*w+x))*((D@@2)(k))(t*w+x)-18*(diff(diff(U(xi), xi), xi))*(D(k))(t*w+x)*w*exp(I*k(t*w+x))*((D@@2)(k))(t*w+x)+10*U(xi)*(D(k))(t*w+x)^3*w*exp(I*k(t*w+x))*((D@@2)(k))(t*w+x)-16*(diff(U(xi), xi))*((D@@3)(k))(t*w+x)*w*(D(k))(t*w+x)*exp(I*k(t*w+x))-5*U(xi)*((D@@4)(k))(t*w+x)*w*(D(k))(t*w+x)*exp(I*k(t*w+x))+(6*I)*(diff(U(xi), xi))*v*(D(k))(t*w+x)^2*exp(I*k(t*w+x))*((D@@2)(k))(t*w+x)-(10*I)*U(xi)*((D@@3)(k))(t*w+x)*w*(D(k))(t*w+x)^2*exp(I*k(t*w+x))-(15*I)*U(xi)*((D@@2)(k))(t*w+x)^2*w*(D(k))(t*w+x)*exp(I*k(t*w+x))-(24*I)*(diff(U(xi), xi))*(D(k))(t*w+x)^2*w*exp(I*k(t*w+x))*((D@@2)(k))(t*w+x))-alpha*s*c[1]*(-(10*I)*(diff(diff(U(xi), xi), xi))*(D(k))(t*w+x)^3*exp(I*k(t*w+x))+(5*I)*(diff(diff(diff(diff(U(xi), xi), xi), xi), xi))*(D(k))(t*w+x)*exp(I*k(t*w+x))+(10*I)*(diff(diff(U(xi), xi), xi))*((D@@3)(k))(t*w+x)*exp(I*k(t*w+x))+I*U(xi)*((D@@5)(k))(t*w+x)*exp(I*k(t*w+x))+I*U(xi)*(D(k))(t*w+x)^5*exp(I*k(t*w+x))-10*U(xi)*((D@@3)(k))(t*w+x)*((D@@2)(k))(t*w+x)*exp(I*k(t*w+x))-15*(diff(U(xi), xi))*((D@@2)(k))(t*w+x)^2*exp(I*k(t*w+x))+10*U(xi)*(D(k))(t*w+x)^3*exp(I*k(t*w+x))*((D@@2)(k))(t*w+x)+(10*I)*(diff(diff(diff(U(xi), xi), xi), xi))*((D@@2)(k))(t*w+x)*exp(I*k(t*w+x))-5*U(xi)*((D@@4)(k))(t*w+x)*(D(k))(t*w+x)*exp(I*k(t*w+x))-20*(diff(U(xi), xi))*((D@@3)(k))(t*w+x)*(D(k))(t*w+x)*exp(I*k(t*w+x))-30*(diff(diff(U(xi), xi), xi))*(D(k))(t*w+x)*exp(I*k(t*w+x))*((D@@2)(k))(t*w+x)+(5*I)*(diff(U(xi), xi))*((D@@4)(k))(t*w+x)*exp(I*k(t*w+x))-(15*I)*U(xi)*((D@@2)(k))(t*w+x)^2*(D(k))(t*w+x)*exp(I*k(t*w+x))-(10*I)*U(xi)*((D@@3)(k))(t*w+x)*(D(k))(t*w+x)^2*exp(I*k(t*w+x))-(30*I)*(diff(U(xi), xi))*(D(k))(t*w+x)^2*exp(I*k(t*w+x))*((D@@2)(k))(t*w+x)+(diff(diff(diff(diff(diff(U(xi), xi), xi), xi), xi), xi))*exp(I*k(t*w+x))+5*(diff(U(xi), xi))*(D(k))(t*w+x)^4*exp(I*k(t*w+x))-10*(diff(diff(diff(U(xi), xi), xi), xi))*(D(k))(t*w+x)^2*exp(I*k(t*w+x)))+c[2]*(-(diff(U(xi), xi))*v*exp(I*k(t*w+x))+I*U(xi)*(D(k))(t*w+x)*w*exp(I*k(t*w+x)))*U(xi)^2-2*exp(I*k(t*w+x))*(diff(U(xi), xi))*U(xi)^2*v*c[2]+c[3]*(-(diff(U(xi), xi))*v*exp(I*k(t*w+x))+I*U(xi)*(D(k))(t*w+x)*w*exp(I*k(t*w+x)))*U(xi)^4-4*exp(I*k(t*w+x))*(diff(U(xi), xi))*U(xi)^4*v*c[3]+c[4]*(-(diff(U(xi), xi))*v*exp(I*k(t*w+x))+I*U(xi)*(D(k))(t*w+x)*w*exp(I*k(t*w+x)))*(2*(diff(U(xi), xi))^2+2*U(xi)*(diff(diff(U(xi), xi), xi)))+c[4]*U(xi)*exp(I*k(t*w+x))*(-6*(diff(U(xi), xi))*(diff(diff(U(xi), xi), xi))*v-2*U(xi)*(diff(diff(diff(U(xi), xi), xi), xi))*v)-beta*s*(-(10*I)*(diff(diff(U(xi), xi), xi))*(D(k))(t*w+x)^3*exp(I*k(t*w+x))+(5*I)*(diff(diff(diff(diff(U(xi), xi), xi), xi), xi))*(D(k))(t*w+x)*exp(I*k(t*w+x))+(10*I)*(diff(diff(U(xi), xi), xi))*((D@@3)(k))(t*w+x)*exp(I*k(t*w+x))+I*U(xi)*((D@@5)(k))(t*w+x)*exp(I*k(t*w+x))+I*U(xi)*(D(k))(t*w+x)^5*exp(I*k(t*w+x))-10*U(xi)*((D@@3)(k))(t*w+x)*((D@@2)(k))(t*w+x)*exp(I*k(t*w+x))-15*(diff(U(xi), xi))*((D@@2)(k))(t*w+x)^2*exp(I*k(t*w+x))+10*U(xi)*(D(k))(t*w+x)^3*exp(I*k(t*w+x))*((D@@2)(k))(t*w+x)+(10*I)*(diff(diff(diff(U(xi), xi), xi), xi))*((D@@2)(k))(t*w+x)*exp(I*k(t*w+x))-5*U(xi)*((D@@4)(k))(t*w+x)*(D(k))(t*w+x)*exp(I*k(t*w+x))-20*(diff(U(xi), xi))*((D@@3)(k))(t*w+x)*(D(k))(t*w+x)*exp(I*k(t*w+x))-30*(diff(diff(U(xi), xi), xi))*(D(k))(t*w+x)*exp(I*k(t*w+x))*((D@@2)(k))(t*w+x)+(5*I)*(diff(U(xi), xi))*((D@@4)(k))(t*w+x)*exp(I*k(t*w+x))-(15*I)*U(xi)*((D@@2)(k))(t*w+x)^2*(D(k))(t*w+x)*exp(I*k(t*w+x))-(10*I)*U(xi)*((D@@3)(k))(t*w+x)*(D(k))(t*w+x)^2*exp(I*k(t*w+x))-(30*I)*(diff(U(xi), xi))*(D(k))(t*w+x)^2*exp(I*k(t*w+x))*((D@@2)(k))(t*w+x)+(diff(diff(diff(diff(diff(U(xi), xi), xi), xi), xi), xi))*exp(I*k(t*w+x))+5*(diff(U(xi), xi))*(D(k))(t*w+x)^4*exp(I*k(t*w+x))-10*(diff(diff(diff(U(xi), xi), xi), xi))*(D(k))(t*w+x)^2*exp(I*k(t*w+x)))+c[2]*((diff(U(xi), xi))*exp(I*k(t*w+x))+I*U(xi)*(D(k))(t*w+x)*exp(I*k(t*w+x)))*U(xi)^2+2*exp(I*k(t*w+x))*(diff(U(xi), xi))*U(xi)^2*c[2]+c[3]*((diff(U(xi), xi))*exp(I*k(t*w+x))+I*U(xi)*(D(k))(t*w+x)*exp(I*k(t*w+x)))*U(xi)^4+4*exp(I*k(t*w+x))*(diff(U(xi), xi))*U(xi)^4*c[3]+c[4]*((diff(U(xi), xi))*exp(I*k(t*w+x))+I*U(xi)*(D(k))(t*w+x)*exp(I*k(t*w+x)))*(2*(diff(U(xi), xi))^2+2*U(xi)*(diff(diff(U(xi), xi), xi)))+c[4]*U(xi)*exp(I*k(t*w+x))*(6*(diff(U(xi), xi))*(diff(diff(U(xi), xi), xi))+2*U(xi)*(diff(diff(diff(U(xi), xi), xi), xi))) = 0))*denom(rhs(I*((diff(diff(U(xi), xi), xi))*v^2*exp(I*k(t*w+x))-(2*I)*(diff(U(xi), xi))*v*(D(k))(t*w+x)*w*exp(I*k(t*w+x))+I*U(xi)*((D@@2)(k))(t*w+x)*w^2*exp(I*k(t*w+x))-U(xi)*(D(k))(t*w+x)^2*w^2*exp(I*k(t*w+x))-s^2*((diff(diff(U(xi), xi), xi))*exp(I*k(t*w+x))+(2*I)*(diff(U(xi), xi))*(D(k))(t*w+x)*exp(I*k(t*w+x))+I*U(xi)*((D@@2)(k))(t*w+x)*exp(I*k(t*w+x))-U(xi)*(D(k))(t*w+x)^2*exp(I*k(t*w+x))))+(1/24)*c[1]*(-(diff(diff(diff(diff(diff(U(xi), xi), xi), xi), xi), xi))*v*exp(I*k(t*w+x))+6*(diff(diff(diff(U(xi), xi), xi), xi))*v*(D(k))(t*w+x)^2*exp(I*k(t*w+x))-4*(diff(diff(diff(U(xi), xi), xi), xi))*(D(k))(t*w+x)^2*w*exp(I*k(t*w+x))+4*(diff(U(xi), xi))*(D(k))(t*w+x)^4*w*exp(I*k(t*w+x))-12*(diff(U(xi), xi))*((D@@2)(k))(t*w+x)^2*w*exp(I*k(t*w+x))+3*(diff(U(xi), xi))*v*((D@@2)(k))(t*w+x)^2*exp(I*k(t*w+x))-(diff(U(xi), xi))*v*(D(k))(t*w+x)^4*exp(I*k(t*w+x))-10*U(xi)*((D@@3)(k))(t*w+x)*w*((D@@2)(k))(t*w+x)*exp(I*k(t*w+x))+4*(diff(U(xi), xi))*v*((D@@3)(k))(t*w+x)*(D(k))(t*w+x)*exp(I*k(t*w+x))-I*(diff(U(xi), xi))*v*((D@@4)(k))(t*w+x)*exp(I*k(t*w+x))-(6*I)*(diff(diff(U(xi), xi), xi))*(D(k))(t*w+x)^3*w*exp(I*k(t*w+x))-(6*I)*(diff(diff(diff(U(xi), xi), xi), xi))*v*((D@@2)(k))(t*w+x)*exp(I*k(t*w+x))-(4*I)*(diff(diff(U(xi), xi), xi))*v*((D@@3)(k))(t*w+x)*exp(I*k(t*w+x))-(4*I)*(diff(diff(diff(diff(U(xi), xi), xi), xi), xi))*v*(D(k))(t*w+x)*exp(I*k(t*w+x))+I*U(xi)*(D(k))(t*w+x)^5*w*exp(I*k(t*w+x))+I*(diff(diff(diff(diff(U(xi), xi), xi), xi), xi))*(D(k))(t*w+x)*w*exp(I*k(t*w+x))+I*U(xi)*((D@@5)(k))(t*w+x)*w*exp(I*k(t*w+x))+(4*I)*(diff(diff(diff(U(xi), xi), xi), xi))*((D@@2)(k))(t*w+x)*w*exp(I*k(t*w+x))+(6*I)*(diff(diff(U(xi), xi), xi))*((D@@3)(k))(t*w+x)*w*exp(I*k(t*w+x))+(4*I)*(diff(U(xi), xi))*((D@@4)(k))(t*w+x)*w*exp(I*k(t*w+x))+(4*I)*(diff(diff(U(xi), xi), xi))*v*(D(k))(t*w+x)^3*exp(I*k(t*w+x))+12*(diff(diff(U(xi), xi), xi))*v*(D(k))(t*w+x)*exp(I*k(t*w+x))*((D@@2)(k))(t*w+x)-18*(diff(diff(U(xi), xi), xi))*(D(k))(t*w+x)*w*exp(I*k(t*w+x))*((D@@2)(k))(t*w+x)+10*U(xi)*(D(k))(t*w+x)^3*w*exp(I*k(t*w+x))*((D@@2)(k))(t*w+x)-16*(diff(U(xi), xi))*((D@@3)(k))(t*w+x)*w*(D(k))(t*w+x)*exp(I*k(t*w+x))-5*U(xi)*((D@@4)(k))(t*w+x)*w*(D(k))(t*w+x)*exp(I*k(t*w+x))+(6*I)*(diff(U(xi), xi))*v*(D(k))(t*w+x)^2*exp(I*k(t*w+x))*((D@@2)(k))(t*w+x)-(10*I)*U(xi)*((D@@3)(k))(t*w+x)*w*(D(k))(t*w+x)^2*exp(I*k(t*w+x))-(15*I)*U(xi)*((D@@2)(k))(t*w+x)^2*w*(D(k))(t*w+x)*exp(I*k(t*w+x))-(24*I)*(diff(U(xi), xi))*(D(k))(t*w+x)^2*w*exp(I*k(t*w+x))*((D@@2)(k))(t*w+x))-alpha*s*c[1]*(-(10*I)*(diff(diff(U(xi), xi), xi))*(D(k))(t*w+x)^3*exp(I*k(t*w+x))+(5*I)*(diff(diff(diff(diff(U(xi), xi), xi), xi), xi))*(D(k))(t*w+x)*exp(I*k(t*w+x))+(10*I)*(diff(diff(U(xi), xi), xi))*((D@@3)(k))(t*w+x)*exp(I*k(t*w+x))+I*U(xi)*((D@@5)(k))(t*w+x)*exp(I*k(t*w+x))+I*U(xi)*(D(k))(t*w+x)^5*exp(I*k(t*w+x))-10*U(xi)*((D@@3)(k))(t*w+x)*((D@@2)(k))(t*w+x)*exp(I*k(t*w+x))-15*(diff(U(xi), xi))*((D@@2)(k))(t*w+x)^2*exp(I*k(t*w+x))+10*U(xi)*(D(k))(t*w+x)^3*exp(I*k(t*w+x))*((D@@2)(k))(t*w+x)+(10*I)*(diff(diff(diff(U(xi), xi), xi), xi))*((D@@2)(k))(t*w+x)*exp(I*k(t*w+x))-5*U(xi)*((D@@4)(k))(t*w+x)*(D(k))(t*w+x)*exp(I*k(t*w+x))-20*(diff(U(xi), xi))*((D@@3)(k))(t*w+x)*(D(k))(t*w+x)*exp(I*k(t*w+x))-30*(diff(diff(U(xi), xi), xi))*(D(k))(t*w+x)*exp(I*k(t*w+x))*((D@@2)(k))(t*w+x)+(5*I)*(diff(U(xi), xi))*((D@@4)(k))(t*w+x)*exp(I*k(t*w+x))-(15*I)*U(xi)*((D@@2)(k))(t*w+x)^2*(D(k))(t*w+x)*exp(I*k(t*w+x))-(10*I)*U(xi)*((D@@3)(k))(t*w+x)*(D(k))(t*w+x)^2*exp(I*k(t*w+x))-(30*I)*(diff(U(xi), xi))*(D(k))(t*w+x)^2*exp(I*k(t*w+x))*((D@@2)(k))(t*w+x)+(diff(diff(diff(diff(diff(U(xi), xi), xi), xi), xi), xi))*exp(I*k(t*w+x))+5*(diff(U(xi), xi))*(D(k))(t*w+x)^4*exp(I*k(t*w+x))-10*(diff(diff(diff(U(xi), xi), xi), xi))*(D(k))(t*w+x)^2*exp(I*k(t*w+x)))+c[2]*(-(diff(U(xi), xi))*v*exp(I*k(t*w+x))+I*U(xi)*(D(k))(t*w+x)*w*exp(I*k(t*w+x)))*U(xi)^2-2*exp(I*k(t*w+x))*(diff(U(xi), xi))*U(xi)^2*v*c[2]+c[3]*(-(diff(U(xi), xi))*v*exp(I*k(t*w+x))+I*U(xi)*(D(k))(t*w+x)*w*exp(I*k(t*w+x)))*U(xi)^4-4*exp(I*k(t*w+x))*(diff(U(xi), xi))*U(xi)^4*v*c[3]+c[4]*(-(diff(U(xi), xi))*v*exp(I*k(t*w+x))+I*U(xi)*(D(k))(t*w+x)*w*exp(I*k(t*w+x)))*(2*(diff(U(xi), xi))^2+2*U(xi)*(diff(diff(U(xi), xi), xi)))+c[4]*U(xi)*exp(I*k(t*w+x))*(-6*(diff(U(xi), xi))*(diff(diff(U(xi), xi), xi))*v-2*U(xi)*(diff(diff(diff(U(xi), xi), xi), xi))*v)-beta*s*(-(10*I)*(diff(diff(U(xi), xi), xi))*(D(k))(t*w+x)^3*exp(I*k(t*w+x))+(5*I)*(diff(diff(diff(diff(U(xi), xi), xi), xi), xi))*(D(k))(t*w+x)*exp(I*k(t*w+x))+(10*I)*(diff(diff(U(xi), xi), xi))*((D@@3)(k))(t*w+x)*exp(I*k(t*w+x))+I*U(xi)*((D@@5)(k))(t*w+x)*exp(I*k(t*w+x))+I*U(xi)*(D(k))(t*w+x)^5*exp(I*k(t*w+x))-10*U(xi)*((D@@3)(k))(t*w+x)*((D@@2)(k))(t*w+x)*exp(I*k(t*w+x))-15*(diff(U(xi), xi))*((D@@2)(k))(t*w+x)^2*exp(I*k(t*w+x))+10*U(xi)*(D(k))(t*w+x)^3*exp(I*k(t*w+x))*((D@@2)(k))(t*w+x)+(10*I)*(diff(diff(diff(U(xi), xi), xi), xi))*((D@@2)(k))(t*w+x)*exp(I*k(t*w+x))-5*U(xi)*((D@@4)(k))(t*w+x)*(D(k))(t*w+x)*exp(I*k(t*w+x))-20*(diff(U(xi), xi))*((D@@3)(k))(t*w+x)*(D(k))(t*w+x)*exp(I*k(t*w+x))-30*(diff(diff(U(xi), xi), xi))*(D(k))(t*w+x)*exp(I*k(t*w+x))*((D@@2)(k))(t*w+x)+(5*I)*(diff(U(xi), xi))*((D@@4)(k))(t*w+x)*exp(I*k(t*w+x))-(15*I)*U(xi)*((D@@2)(k))(t*w+x)^2*(D(k))(t*w+x)*exp(I*k(t*w+x))-(10*I)*U(xi)*((D@@3)(k))(t*w+x)*(D(k))(t*w+x)^2*exp(I*k(t*w+x))-(30*I)*(diff(U(xi), xi))*(D(k))(t*w+x)^2*exp(I*k(t*w+x))*((D@@2)(k))(t*w+x)+(diff(diff(diff(diff(diff(U(xi), xi), xi), xi), xi), xi))*exp(I*k(t*w+x))+5*(diff(U(xi), xi))*(D(k))(t*w+x)^4*exp(I*k(t*w+x))-10*(diff(diff(diff(U(xi), xi), xi), xi))*(D(k))(t*w+x)^2*exp(I*k(t*w+x)))+c[2]*((diff(U(xi), xi))*exp(I*k(t*w+x))+I*U(xi)*(D(k))(t*w+x)*exp(I*k(t*w+x)))*U(xi)^2+2*exp(I*k(t*w+x))*(diff(U(xi), xi))*U(xi)^2*c[2]+c[3]*((diff(U(xi), xi))*exp(I*k(t*w+x))+I*U(xi)*(D(k))(t*w+x)*exp(I*k(t*w+x)))*U(xi)^4+4*exp(I*k(t*w+x))*(diff(U(xi), xi))*U(xi)^4*c[3]+c[4]*((diff(U(xi), xi))*exp(I*k(t*w+x))+I*U(xi)*(D(k))(t*w+x)*exp(I*k(t*w+x)))*(2*(diff(U(xi), xi))^2+2*U(xi)*(diff(diff(U(xi), xi), xi)))+c[4]*U(xi)*exp(I*k(t*w+x))*(6*(diff(U(xi), xi))*(diff(diff(U(xi), xi), xi))+2*U(xi)*(diff(diff(diff(U(xi), xi), xi), xi))) = 0)) = numer(rhs(I*((diff(diff(U(xi), xi), xi))*v^2*exp(I*k(t*w+x))-(2*I)*(diff(U(xi), xi))*v*(D(k))(t*w+x)*w*exp(I*k(t*w+x))+I*U(xi)*((D@@2)(k))(t*w+x)*w^2*exp(I*k(t*w+x))-U(xi)*(D(k))(t*w+x)^2*w^2*exp(I*k(t*w+x))-s^2*((diff(diff(U(xi), xi), xi))*exp(I*k(t*w+x))+(2*I)*(diff(U(xi), xi))*(D(k))(t*w+x)*exp(I*k(t*w+x))+I*U(xi)*((D@@2)(k))(t*w+x)*exp(I*k(t*w+x))-U(xi)*(D(k))(t*w+x)^2*exp(I*k(t*w+x))))+(1/24)*c[1]*(-(diff(diff(diff(diff(diff(U(xi), xi), xi), xi), xi), xi))*v*exp(I*k(t*w+x))+6*(diff(diff(diff(U(xi), xi), xi), xi))*v*(D(k))(t*w+x)^2*exp(I*k(t*w+x))-4*(diff(diff(diff(U(xi), xi), xi), xi))*(D(k))(t*w+x)^2*w*exp(I*k(t*w+x))+4*(diff(U(xi), xi))*(D(k))(t*w+x)^4*w*exp(I*k(t*w+x))-12*(diff(U(xi), xi))*((D@@2)(k))(t*w+x)^2*w*exp(I*k(t*w+x))+3*(diff(U(xi), xi))*v*((D@@2)(k))(t*w+x)^2*exp(I*k(t*w+x))-(diff(U(xi), xi))*v*(D(k))(t*w+x)^4*exp(I*k(t*w+x))-10*U(xi)*((D@@3)(k))(t*w+x)*w*((D@@2)(k))(t*w+x)*exp(I*k(t*w+x))+4*(diff(U(xi), xi))*v*((D@@3)(k))(t*w+x)*(D(k))(t*w+x)*exp(I*k(t*w+x))-I*(diff(U(xi), xi))*v*((D@@4)(k))(t*w+x)*exp(I*k(t*w+x))-(6*I)*(diff(diff(U(xi), xi), xi))*(D(k))(t*w+x)^3*w*exp(I*k(t*w+x))-(6*I)*(diff(diff(diff(U(xi), xi), xi), xi))*v*((D@@2)(k))(t*w+x)*exp(I*k(t*w+x))-(4*I)*(diff(diff(U(xi), xi), xi))*v*((D@@3)(k))(t*w+x)*exp(I*k(t*w+x))-(4*I)*(diff(diff(diff(diff(U(xi), xi), xi), xi), xi))*v*(D(k))(t*w+x)*exp(I*k(t*w+x))+I*U(xi)*(D(k))(t*w+x)^5*w*exp(I*k(t*w+x))+I*(diff(diff(diff(diff(U(xi), xi), xi), xi), xi))*(D(k))(t*w+x)*w*exp(I*k(t*w+x))+I*U(xi)*((D@@5)(k))(t*w+x)*w*exp(I*k(t*w+x))+(4*I)*(diff(diff(diff(U(xi), xi), xi), xi))*((D@@2)(k))(t*w+x)*w*exp(I*k(t*w+x))+(6*I)*(diff(diff(U(xi), xi), xi))*((D@@3)(k))(t*w+x)*w*exp(I*k(t*w+x))+(4*I)*(diff(U(xi), xi))*((D@@4)(k))(t*w+x)*w*exp(I*k(t*w+x))+(4*I)*(diff(diff(U(xi), xi), xi))*v*(D(k))(t*w+x)^3*exp(I*k(t*w+x))+12*(diff(diff(U(xi), xi), xi))*v*(D(k))(t*w+x)*exp(I*k(t*w+x))*((D@@2)(k))(t*w+x)-18*(diff(diff(U(xi), xi), xi))*(D(k))(t*w+x)*w*exp(I*k(t*w+x))*((D@@2)(k))(t*w+x)+10*U(xi)*(D(k))(t*w+x)^3*w*exp(I*k(t*w+x))*((D@@2)(k))(t*w+x)-16*(diff(U(xi), xi))*((D@@3)(k))(t*w+x)*w*(D(k))(t*w+x)*exp(I*k(t*w+x))-5*U(xi)*((D@@4)(k))(t*w+x)*w*(D(k))(t*w+x)*exp(I*k(t*w+x))+(6*I)*(diff(U(xi), xi))*v*(D(k))(t*w+x)^2*exp(I*k(t*w+x))*((D@@2)(k))(t*w+x)-(10*I)*U(xi)*((D@@3)(k))(t*w+x)*w*(D(k))(t*w+x)^2*exp(I*k(t*w+x))-(15*I)*U(xi)*((D@@2)(k))(t*w+x)^2*w*(D(k))(t*w+x)*exp(I*k(t*w+x))-(24*I)*(diff(U(xi), xi))*(D(k))(t*w+x)^2*w*exp(I*k(t*w+x))*((D@@2)(k))(t*w+x))-alpha*s*c[1]*(-(10*I)*(diff(diff(U(xi), xi), xi))*(D(k))(t*w+x)^3*exp(I*k(t*w+x))+(5*I)*(diff(diff(diff(diff(U(xi), xi), xi), xi), xi))*(D(k))(t*w+x)*exp(I*k(t*w+x))+(10*I)*(diff(diff(U(xi), xi), xi))*((D@@3)(k))(t*w+x)*exp(I*k(t*w+x))+I*U(xi)*((D@@5)(k))(t*w+x)*exp(I*k(t*w+x))+I*U(xi)*(D(k))(t*w+x)^5*exp(I*k(t*w+x))-10*U(xi)*((D@@3)(k))(t*w+x)*((D@@2)(k))(t*w+x)*exp(I*k(t*w+x))-15*(diff(U(xi), xi))*((D@@2)(k))(t*w+x)^2*exp(I*k(t*w+x))+10*U(xi)*(D(k))(t*w+x)^3*exp(I*k(t*w+x))*((D@@2)(k))(t*w+x)+(10*I)*(diff(diff(diff(U(xi), xi), xi), xi))*((D@@2)(k))(t*w+x)*exp(I*k(t*w+x))-5*U(xi)*((D@@4)(k))(t*w+x)*(D(k))(t*w+x)*exp(I*k(t*w+x))-20*(diff(U(xi), xi))*((D@@3)(k))(t*w+x)*(D(k))(t*w+x)*exp(I*k(t*w+x))-30*(diff(diff(U(xi), xi), xi))*(D(k))(t*w+x)*exp(I*k(t*w+x))*((D@@2)(k))(t*w+x)+(5*I)*(diff(U(xi), xi))*((D@@4)(k))(t*w+x)*exp(I*k(t*w+x))-(15*I)*U(xi)*((D@@2)(k))(t*w+x)^2*(D(k))(t*w+x)*exp(I*k(t*w+x))-(10*I)*U(xi)*((D@@3)(k))(t*w+x)*(D(k))(t*w+x)^2*exp(I*k(t*w+x))-(30*I)*(diff(U(xi), xi))*(D(k))(t*w+x)^2*exp(I*k(t*w+x))*((D@@2)(k))(t*w+x)+(diff(diff(diff(diff(diff(U(xi), xi), xi), xi), xi), xi))*exp(I*k(t*w+x))+5*(diff(U(xi), xi))*(D(k))(t*w+x)^4*exp(I*k(t*w+x))-10*(diff(diff(diff(U(xi), xi), xi), xi))*(D(k))(t*w+x)^2*exp(I*k(t*w+x)))+c[2]*(-(diff(U(xi), xi))*v*exp(I*k(t*w+x))+I*U(xi)*(D(k))(t*w+x)*w*exp(I*k(t*w+x)))*U(xi)^2-2*exp(I*k(t*w+x))*(diff(U(xi), xi))*U(xi)^2*v*c[2]+c[3]*(-(diff(U(xi), xi))*v*exp(I*k(t*w+x))+I*U(xi)*(D(k))(t*w+x)*w*exp(I*k(t*w+x)))*U(xi)^4-4*exp(I*k(t*w+x))*(diff(U(xi), xi))*U(xi)^4*v*c[3]+c[4]*(-(diff(U(xi), xi))*v*exp(I*k(t*w+x))+I*U(xi)*(D(k))(t*w+x)*w*exp(I*k(t*w+x)))*(2*(diff(U(xi), xi))^2+2*U(xi)*(diff(diff(U(xi), xi), xi)))+c[4]*U(xi)*exp(I*k(t*w+x))*(-6*(diff(U(xi), xi))*(diff(diff(U(xi), xi), xi))*v-2*U(xi)*(diff(diff(diff(U(xi), xi), xi), xi))*v)-beta*s*(-(10*I)*(diff(diff(U(xi), xi), xi))*(D(k))(t*w+x)^3*exp(I*k(t*w+x))+(5*I)*(diff(diff(diff(diff(U(xi), xi), xi), xi), xi))*(D(k))(t*w+x)*exp(I*k(t*w+x))+(10*I)*(diff(diff(U(xi), xi), xi))*((D@@3)(k))(t*w+x)*exp(I*k(t*w+x))+I*U(xi)*((D@@5)(k))(t*w+x)*exp(I*k(t*w+x))+I*U(xi)*(D(k))(t*w+x)^5*exp(I*k(t*w+x))-10*U(xi)*((D@@3)(k))(t*w+x)*((D@@2)(k))(t*w+x)*exp(I*k(t*w+x))-15*(diff(U(xi), xi))*((D@@2)(k))(t*w+x)^2*exp(I*k(t*w+x))+10*U(xi)*(D(k))(t*w+x)^3*exp(I*k(t*w+x))*((D@@2)(k))(t*w+x)+(10*I)*(diff(diff(diff(U(xi), xi), xi), xi))*((D@@2)(k))(t*w+x)*exp(I*k(t*w+x))-5*U(xi)*((D@@4)(k))(t*w+x)*(D(k))(t*w+x)*exp(I*k(t*w+x))-20*(diff(U(xi), xi))*((D@@3)(k))(t*w+x)*(D(k))(t*w+x)*exp(I*k(t*w+x))-30*(diff(diff(U(xi), xi), xi))*(D(k))(t*w+x)*exp(I*k(t*w+x))*((D@@2)(k))(t*w+x)+(5*I)*(diff(U(xi), xi))*((D@@4)(k))(t*w+x)*exp(I*k(t*w+x))-(15*I)*U(xi)*((D@@2)(k))(t*w+x)^2*(D(k))(t*w+x)*exp(I*k(t*w+x))-(10*I)*U(xi)*((D@@3)(k))(t*w+x)*(D(k))(t*w+x)^2*exp(I*k(t*w+x))-(30*I)*(diff(U(xi), xi))*(D(k))(t*w+x)^2*exp(I*k(t*w+x))*((D@@2)(k))(t*w+x)+(diff(diff(diff(diff(diff(U(xi), xi), xi), xi), xi), xi))*exp(I*k(t*w+x))+5*(diff(U(xi), xi))*(D(k))(t*w+x)^4*exp(I*k(t*w+x))-10*(diff(diff(diff(U(xi), xi), xi), xi))*(D(k))(t*w+x)^2*exp(I*k(t*w+x)))+c[2]*((diff(U(xi), xi))*exp(I*k(t*w+x))+I*U(xi)*(D(k))(t*w+x)*exp(I*k(t*w+x)))*U(xi)^2+2*exp(I*k(t*w+x))*(diff(U(xi), xi))*U(xi)^2*c[2]+c[3]*((diff(U(xi), xi))*exp(I*k(t*w+x))+I*U(xi)*(D(k))(t*w+x)*exp(I*k(t*w+x)))*U(xi)^4+4*exp(I*k(t*w+x))*(diff(U(xi), xi))*U(xi)^4*c[3]+c[4]*((diff(U(xi), xi))*exp(I*k(t*w+x))+I*U(xi)*(D(k))(t*w+x)*exp(I*k(t*w+x)))*(2*(diff(U(xi), xi))^2+2*U(xi)*(diff(diff(U(xi), xi), xi)))+c[4]*U(xi)*exp(I*k(t*w+x))*(6*(diff(U(xi), xi))*(diff(diff(U(xi), xi), xi))+2*U(xi)*(diff(diff(diff(U(xi), xi), xi), xi))) = 0))*denom(lhs(I*((diff(diff(U(xi), xi), xi))*v^2*exp(I*k(t*w+x))-(2*I)*(diff(U(xi), xi))*v*(D(k))(t*w+x)*w*exp(I*k(t*w+x))+I*U(xi)*((D@@2)(k))(t*w+x)*w^2*exp(I*k(t*w+x))-U(xi)*(D(k))(t*w+x)^2*w^2*exp(I*k(t*w+x))-s^2*((diff(diff(U(xi), xi), xi))*exp(I*k(t*w+x))+(2*I)*(diff(U(xi), xi))*(D(k))(t*w+x)*exp(I*k(t*w+x))+I*U(xi)*((D@@2)(k))(t*w+x)*exp(I*k(t*w+x))-U(xi)*(D(k))(t*w+x)^2*exp(I*k(t*w+x))))+(1/24)*c[1]*(-(diff(diff(diff(diff(diff(U(xi), xi), xi), xi), xi), xi))*v*exp(I*k(t*w+x))+6*(diff(diff(diff(U(xi), xi), xi), xi))*v*(D(k))(t*w+x)^2*exp(I*k(t*w+x))-4*(diff(diff(diff(U(xi), xi), xi), xi))*(D(k))(t*w+x)^2*w*exp(I*k(t*w+x))+4*(diff(U(xi), xi))*(D(k))(t*w+x)^4*w*exp(I*k(t*w+x))-12*(diff(U(xi), xi))*((D@@2)(k))(t*w+x)^2*w*exp(I*k(t*w+x))+3*(diff(U(xi), xi))*v*((D@@2)(k))(t*w+x)^2*exp(I*k(t*w+x))-(diff(U(xi), xi))*v*(D(k))(t*w+x)^4*exp(I*k(t*w+x))-10*U(xi)*((D@@3)(k))(t*w+x)*w*((D@@2)(k))(t*w+x)*exp(I*k(t*w+x))+4*(diff(U(xi), xi))*v*((D@@3)(k))(t*w+x)*(D(k))(t*w+x)*exp(I*k(t*w+x))-I*(diff(U(xi), xi))*v*((D@@4)(k))(t*w+x)*exp(I*k(t*w+x))-(6*I)*(diff(diff(U(xi), xi), xi))*(D(k))(t*w+x)^3*w*exp(I*k(t*w+x))-(6*I)*(diff(diff(diff(U(xi), xi), xi), xi))*v*((D@@2)(k))(t*w+x)*exp(I*k(t*w+x))-(4*I)*(diff(diff(U(xi), xi), xi))*v*((D@@3)(k))(t*w+x)*exp(I*k(t*w+x))-(4*I)*(diff(diff(diff(diff(U(xi), xi), xi), xi), xi))*v*(D(k))(t*w+x)*exp(I*k(t*w+x))+I*U(xi)*(D(k))(t*w+x)^5*w*exp(I*k(t*w+x))+I*(diff(diff(diff(diff(U(xi), xi), xi), xi), xi))*(D(k))(t*w+x)*w*exp(I*k(t*w+x))+I*U(xi)*((D@@5)(k))(t*w+x)*w*exp(I*k(t*w+x))+(4*I)*(diff(diff(diff(U(xi), xi), xi), xi))*((D@@2)(k))(t*w+x)*w*exp(I*k(t*w+x))+(6*I)*(diff(diff(U(xi), xi), xi))*((D@@3)(k))(t*w+x)*w*exp(I*k(t*w+x))+(4*I)*(diff(U(xi), xi))*((D@@4)(k))(t*w+x)*w*exp(I*k(t*w+x))+(4*I)*(diff(diff(U(xi), xi), xi))*v*(D(k))(t*w+x)^3*exp(I*k(t*w+x))+12*(diff(diff(U(xi), xi), xi))*v*(D(k))(t*w+x)*exp(I*k(t*w+x))*((D@@2)(k))(t*w+x)-18*(diff(diff(U(xi), xi), xi))*(D(k))(t*w+x)*w*exp(I*k(t*w+x))*((D@@2)(k))(t*w+x)+10*U(xi)*(D(k))(t*w+x)^3*w*exp(I*k(t*w+x))*((D@@2)(k))(t*w+x)-16*(diff(U(xi), xi))*((D@@3)(k))(t*w+x)*w*(D(k))(t*w+x)*exp(I*k(t*w+x))-5*U(xi)*((D@@4)(k))(t*w+x)*w*(D(k))(t*w+x)*exp(I*k(t*w+x))+(6*I)*(diff(U(xi), xi))*v*(D(k))(t*w+x)^2*exp(I*k(t*w+x))*((D@@2)(k))(t*w+x)-(10*I)*U(xi)*((D@@3)(k))(t*w+x)*w*(D(k))(t*w+x)^2*exp(I*k(t*w+x))-(15*I)*U(xi)*((D@@2)(k))(t*w+x)^2*w*(D(k))(t*w+x)*exp(I*k(t*w+x))-(24*I)*(diff(U(xi), xi))*(D(k))(t*w+x)^2*w*exp(I*k(t*w+x))*((D@@2)(k))(t*w+x))-alpha*s*c[1]*(-(10*I)*(diff(diff(U(xi), xi), xi))*(D(k))(t*w+x)^3*exp(I*k(t*w+x))+(5*I)*(diff(diff(diff(diff(U(xi), xi), xi), xi), xi))*(D(k))(t*w+x)*exp(I*k(t*w+x))+(10*I)*(diff(diff(U(xi), xi), xi))*((D@@3)(k))(t*w+x)*exp(I*k(t*w+x))+I*U(xi)*((D@@5)(k))(t*w+x)*exp(I*k(t*w+x))+I*U(xi)*(D(k))(t*w+x)^5*exp(I*k(t*w+x))-10*U(xi)*((D@@3)(k))(t*w+x)*((D@@2)(k))(t*w+x)*exp(I*k(t*w+x))-15*(diff(U(xi), xi))*((D@@2)(k))(t*w+x)^2*exp(I*k(t*w+x))+10*U(xi)*(D(k))(t*w+x)^3*exp(I*k(t*w+x))*((D@@2)(k))(t*w+x)+(10*I)*(diff(diff(diff(U(xi), xi), xi), xi))*((D@@2)(k))(t*w+x)*exp(I*k(t*w+x))-5*U(xi)*((D@@4)(k))(t*w+x)*(D(k))(t*w+x)*exp(I*k(t*w+x))-20*(diff(U(xi), xi))*((D@@3)(k))(t*w+x)*(D(k))(t*w+x)*exp(I*k(t*w+x))-30*(diff(diff(U(xi), xi), xi))*(D(k))(t*w+x)*exp(I*k(t*w+x))*((D@@2)(k))(t*w+x)+(5*I)*(diff(U(xi), xi))*((D@@4)(k))(t*w+x)*exp(I*k(t*w+x))-(15*I)*U(xi)*((D@@2)(k))(t*w+x)^2*(D(k))(t*w+x)*exp(I*k(t*w+x))-(10*I)*U(xi)*((D@@3)(k))(t*w+x)*(D(k))(t*w+x)^2*exp(I*k(t*w+x))-(30*I)*(diff(U(xi), xi))*(D(k))(t*w+x)^2*exp(I*k(t*w+x))*((D@@2)(k))(t*w+x)+(diff(diff(diff(diff(diff(U(xi), xi), xi), xi), xi), xi))*exp(I*k(t*w+x))+5*(diff(U(xi), xi))*(D(k))(t*w+x)^4*exp(I*k(t*w+x))-10*(diff(diff(diff(U(xi), xi), xi), xi))*(D(k))(t*w+x)^2*exp(I*k(t*w+x)))+c[2]*(-(diff(U(xi), xi))*v*exp(I*k(t*w+x))+I*U(xi)*(D(k))(t*w+x)*w*exp(I*k(t*w+x)))*U(xi)^2-2*exp(I*k(t*w+x))*(diff(U(xi), xi))*U(xi)^2*v*c[2]+c[3]*(-(diff(U(xi), xi))*v*exp(I*k(t*w+x))+I*U(xi)*(D(k))(t*w+x)*w*exp(I*k(t*w+x)))*U(xi)^4-4*exp(I*k(t*w+x))*(diff(U(xi), xi))*U(xi)^4*v*c[3]+c[4]*(-(diff(U(xi), xi))*v*exp(I*k(t*w+x))+I*U(xi)*(D(k))(t*w+x)*w*exp(I*k(t*w+x)))*(2*(diff(U(xi), xi))^2+2*U(xi)*(diff(diff(U(xi), xi), xi)))+c[4]*U(xi)*exp(I*k(t*w+x))*(-6*(diff(U(xi), xi))*(diff(diff(U(xi), xi), xi))*v-2*U(xi)*(diff(diff(diff(U(xi), xi), xi), xi))*v)-beta*s*(-(10*I)*(diff(diff(U(xi), xi), xi))*(D(k))(t*w+x)^3*exp(I*k(t*w+x))+(5*I)*(diff(diff(diff(diff(U(xi), xi), xi), xi), xi))*(D(k))(t*w+x)*exp(I*k(t*w+x))+(10*I)*(diff(diff(U(xi), xi), xi))*((D@@3)(k))(t*w+x)*exp(I*k(t*w+x))+I*U(xi)*((D@@5)(k))(t*w+x)*exp(I*k(t*w+x))+I*U(xi)*(D(k))(t*w+x)^5*exp(I*k(t*w+x))-10*U(xi)*((D@@3)(k))(t*w+x)*((D@@2)(k))(t*w+x)*exp(I*k(t*w+x))-15*(diff(U(xi), xi))*((D@@2)(k))(t*w+x)^2*exp(I*k(t*w+x))+10*U(xi)*(D(k))(t*w+x)^3*exp(I*k(t*w+x))*((D@@2)(k))(t*w+x)+(10*I)*(diff(diff(diff(U(xi), xi), xi), xi))*((D@@2)(k))(t*w+x)*exp(I*k(t*w+x))-5*U(xi)*((D@@4)(k))(t*w+x)*(D(k))(t*w+x)*exp(I*k(t*w+x))-20*(diff(U(xi), xi))*((D@@3)(k))(t*w+x)*(D(k))(t*w+x)*exp(I*k(t*w+x))-30*(diff(diff(U(xi), xi), xi))*(D(k))(t*w+x)*exp(I*k(t*w+x))*((D@@2)(k))(t*w+x)+(5*I)*(diff(U(xi), xi))*((D@@4)(k))(t*w+x)*exp(I*k(t*w+x))-(15*I)*U(xi)*((D@@2)(k))(t*w+x)^2*(D(k))(t*w+x)*exp(I*k(t*w+x))-(10*I)*U(xi)*((D@@3)(k))(t*w+x)*(D(k))(t*w+x)^2*exp(I*k(t*w+x))-(30*I)*(diff(U(xi), xi))*(D(k))(t*w+x)^2*exp(I*k(t*w+x))*((D@@2)(k))(t*w+x)+(diff(diff(diff(diff(diff(U(xi), xi), xi), xi), xi), xi))*exp(I*k(t*w+x))+5*(diff(U(xi), xi))*(D(k))(t*w+x)^4*exp(I*k(t*w+x))-10*(diff(diff(diff(U(xi), xi), xi), xi))*(D(k))(t*w+x)^2*exp(I*k(t*w+x)))+c[2]*((diff(U(xi), xi))*exp(I*k(t*w+x))+I*U(xi)*(D(k))(t*w+x)*exp(I*k(t*w+x)))*U(xi)^2+2*exp(I*k(t*w+x))*(diff(U(xi), xi))*U(xi)^2*c[2]+c[3]*((diff(U(xi), xi))*exp(I*k(t*w+x))+I*U(xi)*(D(k))(t*w+x)*exp(I*k(t*w+x)))*U(xi)^4+4*exp(I*k(t*w+x))*(diff(U(xi), xi))*U(xi)^4*c[3]+c[4]*((diff(U(xi), xi))*exp(I*k(t*w+x))+I*U(xi)*(D(k))(t*w+x)*exp(I*k(t*w+x)))*(2*(diff(U(xi), xi))^2+2*U(xi)*(diff(diff(U(xi), xi), xi)))+c[4]*U(xi)*exp(I*k(t*w+x))*(6*(diff(U(xi), xi))*(diff(diff(U(xi), xi), xi))+2*U(xi)*(diff(diff(diff(U(xi), xi), xi), xi))) = 0))

-exp(I*k(t*w+x))*(-I*U(xi)*(D(k))(t*w+x)^5*c[1]*w-(4*I)*(diff(diff(U(xi), xi), xi))*(D(k))(t*w+x)^3*c[1]*v+(6*I)*c[1]*w*(D(k))(t*w+x)^3*(diff(diff(U(xi), xi), xi))+(4*I)*c[1]*v*((D@@3)(k))(t*w+x)*(diff(diff(U(xi), xi), xi))-(6*I)*((D@@3)(k))(t*w+x)*(diff(diff(U(xi), xi), xi))*c[1]*w-(4*I)*((D@@4)(k))(t*w+x)*(diff(U(xi), xi))*c[1]*w+(4*I)*c[1]*v*(diff(diff(diff(diff(U(xi), xi), xi), xi), xi))*(D(k))(t*w+x)-I*(diff(diff(diff(diff(U(xi), xi), xi), xi), xi))*(D(k))(t*w+x)*c[1]*w-I*U(xi)*((D@@5)(k))(t*w+x)*c[1]*w+(6*I)*c[1]*v*(diff(diff(diff(U(xi), xi), xi), xi))*((D@@2)(k))(t*w+x)-(4*I)*(diff(diff(diff(U(xi), xi), xi), xi))*((D@@2)(k))(t*w+x)*c[1]*w+(24*I)*s*beta*U(xi)*(D(k))(t*w+x)^5-(240*I)*(diff(diff(U(xi), xi), xi))*(D(k))(t*w+x)^3*beta*s+(240*I)*s*beta*((D@@3)(k))(t*w+x)*(diff(diff(U(xi), xi), xi))+(120*I)*s*beta*((D@@4)(k))(t*w+x)*(diff(U(xi), xi))+(120*I)*s*beta*(diff(diff(diff(diff(U(xi), xi), xi), xi), xi))*(D(k))(t*w+x)+(24*I)*s*beta*((D@@5)(k))(t*w+x)*U(xi)+(240*I)*s*beta*(diff(diff(diff(U(xi), xi), xi), xi))*((D@@2)(k))(t*w+x)-(48*I)*U(xi)^2*(diff(diff(U(xi), xi), xi))*(D(k))(t*w+x)*c[4]-(48*I)*U(xi)*(diff(U(xi), xi))^2*(D(k))(t*w+x)*c[4]-(24*I)*c[2]*w*U(xi)^3*(D(k))(t*w+x)-(24*I)*c[3]*w*U(xi)^5*(D(k))(t*w+x)+24*c[1]*s*alpha*(diff(diff(diff(diff(diff(U(xi), xi), xi), xi), xi), xi))+48*c[4]*v*(diff(diff(diff(U(xi), xi), xi), xi))*U(xi)^2+c[1]*v*(diff(diff(diff(diff(diff(U(xi), xi), xi), xi), xi), xi))+24*s*beta*(diff(diff(diff(diff(diff(U(xi), xi), xi), xi), xi), xi))-48*c[4]*(diff(diff(diff(U(xi), xi), xi), xi))*U(xi)^2+I*c[1]*v*((D@@4)(k))(t*w+x)*(diff(U(xi), xi))-10*c[1]*w*((D@@2)(k))(t*w+x)*U(xi)*(D(k))(t*w+x)^3-12*c[1]*v*((D@@2)(k))(t*w+x)*(D(k))(t*w+x)*(diff(diff(U(xi), xi), xi))+18*c[1]*w*((D@@2)(k))(t*w+x)*(D(k))(t*w+x)*(diff(diff(U(xi), xi), xi))-4*c[1]*v*((D@@3)(k))(t*w+x)*(D(k))(t*w+x)*(diff(U(xi), xi))+16*c[1]*w*((D@@3)(k))(t*w+x)*(D(k))(t*w+x)*(diff(U(xi), xi))+5*c[1]*w*((D@@4)(k))(t*w+x)*U(xi)*(D(k))(t*w+x)+10*c[1]*w*((D@@3)(k))(t*w+x)*((D@@2)(k))(t*w+x)*U(xi)+120*c[1]*s*alpha*(D(k))(t*w+x)^4*(diff(U(xi), xi))-360*c[1]*s*alpha*((D@@2)(k))(t*w+x)^2*(diff(U(xi), xi))-240*c[1]*s*alpha*(diff(diff(diff(U(xi), xi), xi), xi))*(D(k))(t*w+x)^2+192*c[4]*v*U(xi)*(diff(U(xi), xi))*(diff(diff(U(xi), xi), xi))+240*s*beta*((D@@2)(k))(t*w+x)*U(xi)*(D(k))(t*w+x)^3-720*s*beta*((D@@2)(k))(t*w+x)*(D(k))(t*w+x)*(diff(diff(U(xi), xi), xi))-480*s*beta*((D@@3)(k))(t*w+x)*(D(k))(t*w+x)*(diff(U(xi), xi))-120*s*beta*((D@@4)(k))(t*w+x)*U(xi)*(D(k))(t*w+x)-240*s*beta*((D@@3)(k))(t*w+x)*((D@@2)(k))(t*w+x)*U(xi)-(240*I)*U(xi)*((D@@3)(k))(t*w+x)*(D(k))(t*w+x)^2*c[1]*alpha*s-(360*I)*U(xi)*(D(k))(t*w+x)*((D@@2)(k))(t*w+x)^2*c[1]*alpha*s-(720*I)*(diff(U(xi), xi))*(D(k))(t*w+x)^2*((D@@2)(k))(t*w+x)*c[1]*alpha*s+240*c[1]*s*alpha*((D@@2)(k))(t*w+x)*U(xi)*(D(k))(t*w+x)^3-720*c[1]*s*alpha*((D@@2)(k))(t*w+x)*(D(k))(t*w+x)*(diff(diff(U(xi), xi), xi))-480*c[1]*s*alpha*((D@@3)(k))(t*w+x)*(D(k))(t*w+x)*(diff(U(xi), xi))-120*c[1]*s*alpha*((D@@4)(k))(t*w+x)*U(xi)*(D(k))(t*w+x)-240*c[1]*s*alpha*((D@@3)(k))(t*w+x)*((D@@2)(k))(t*w+x)*U(xi)+(15*I)*c[1]*w*((D@@2)(k))(t*w+x)^2*U(xi)*(D(k))(t*w+x)+(24*I)*c[1]*s*alpha*U(xi)*(D(k))(t*w+x)^5-(240*I)*(diff(diff(U(xi), xi), xi))*(D(k))(t*w+x)^3*c[1]*alpha*s+(240*I)*c[1]*s*alpha*((D@@3)(k))(t*w+x)*(diff(diff(U(xi), xi), xi))+(120*I)*c[1]*s*alpha*((D@@4)(k))(t*w+x)*(diff(U(xi), xi))+(120*I)*c[1]*s*alpha*(diff(diff(diff(diff(U(xi), xi), xi), xi), xi))*(D(k))(t*w+x)+(24*I)*c[1]*s*alpha*((D@@5)(k))(t*w+x)*U(xi)+(240*I)*c[1]*s*alpha*(diff(diff(diff(U(xi), xi), xi), xi))*((D@@2)(k))(t*w+x)-(48*I)*U(xi)^2*(diff(diff(U(xi), xi), xi))*(D(k))(t*w+x)*c[4]*w-48*c[4]*(diff(U(xi), xi))^3-(48*I)*U(xi)*(diff(U(xi), xi))^2*(D(k))(t*w+x)*c[4]*w-(720*I)*(diff(U(xi), xi))*(D(k))(t*w+x)^2*((D@@2)(k))(t*w+x)*beta*s-(240*I)*U(xi)*((D@@3)(k))(t*w+x)*(D(k))(t*w+x)^2*beta*s-(360*I)*U(xi)*(D(k))(t*w+x)*((D@@2)(k))(t*w+x)^2*beta*s-(6*I)*(diff(U(xi), xi))*(D(k))(t*w+x)^2*((D@@2)(k))(t*w+x)*c[1]*v+(24*I)*c[1]*w*((D@@2)(k))(t*w+x)*(D(k))(t*w+x)^2*(diff(U(xi), xi))+(10*I)*c[1]*w*((D@@3)(k))(t*w+x)*U(xi)*(D(k))(t*w+x)^2-(24*I)*s^2*U(xi)*(D(k))(t*w+x)^2-(24*I)*c[2]*U(xi)^3*(D(k))(t*w+x)-(24*I)*c[3]*U(xi)^5*(D(k))(t*w+x)+(24*I)*w^2*U(xi)*(D(k))(t*w+x)^2+24*w^2*((D@@2)(k))(t*w+x)*U(xi)+c[1]*v*(D(k))(t*w+x)^4*(diff(U(xi), xi))-4*c[1]*w*(D(k))(t*w+x)^4*(diff(U(xi), xi))-3*c[1]*v*((D@@2)(k))(t*w+x)^2*(diff(U(xi), xi))+12*c[1]*w*((D@@2)(k))(t*w+x)^2*(diff(U(xi), xi))-6*c[1]*v*(diff(diff(diff(U(xi), xi), xi), xi))*(D(k))(t*w+x)^2+4*c[1]*w*(diff(diff(diff(U(xi), xi), xi), xi))*(D(k))(t*w+x)^2+72*c[2]*v*U(xi)^2*(diff(U(xi), xi))+120*c[3]*v*U(xi)^4*(diff(U(xi), xi))+120*s*beta*(D(k))(t*w+x)^4*(diff(U(xi), xi))-360*s*beta*((D@@2)(k))(t*w+x)^2*(diff(U(xi), xi))-240*s*beta*(diff(diff(diff(U(xi), xi), xi), xi))*(D(k))(t*w+x)^2-192*c[4]*U(xi)*(diff(U(xi), xi))*(diff(diff(U(xi), xi), xi))-48*w*(D(k))(t*w+x)*v*(diff(U(xi), xi))-(24*I)*v^2*(diff(diff(U(xi), xi), xi))+(24*I)*s^2*(diff(diff(U(xi), xi), xi))-48*s^2*(D(k))(t*w+x)*(diff(U(xi), xi))-24*s^2*((D@@2)(k))(t*w+x)*U(xi)+48*c[4]*v*(diff(U(xi), xi))^3-72*c[2]*U(xi)^2*(diff(U(xi), xi))-120*c[3]*U(xi)^4*(diff(U(xi), xi))) = 0

 (10)
> 

%/(-exp(I*k(t*w+x)))

-()/exp(k(t*w+x)*I)

 (11)
 

``

Download tr.mw

Formatting equations for LaTeX output...

Asked by: salim-barzani 1410
latex simplification
May 06 2025
0  8

I want to convert my code output into LaTeX format, but the current formatting isn't suitable for presentation. For example, when I use simplify, it sometimes introduces unnecessary fractions, making the expression look cluttered and less elegant on paper. I'm looking for a way to simplify expressions preferably by factoring terms, without introducing extra fractions, so the final LaTeX result appears clean and well-structured.

> 

restart
> 

with(PDEtools)
> 

with(LinearAlgebra)
> 

NULL
> 

with(SolveTools)
> 

undeclare(prime)

`There is no more prime differentiation variable; all derivatives will be displayed as indexed functions`

 (1)
> 

declare(u(x, t)); declare(U(xi)); declare(V(xi))

u(x, t)*`will now be displayed as`*u

  

U(xi)*`will now be displayed as`*U

  

V(xi)*`will now be displayed as`*V

 (2)
> 

``
> 

RR := (2*v*(1/3)+2*alpha*beta*(1/3))*U(xi)^3+(-3*alpha*k^2*lambda-4*alpha^2*k-k^2*v+2*k^2*w-4*k*v*w)*U(xi)+(alpha*lambda+v)*(diff(diff(U(xi), xi), xi)) = 0

((2/3)*v+(2/3)*alpha*beta)*U(xi)^3+(-3*alpha*k^2*lambda-4*alpha^2*k-k^2*v+2*k^2*w-4*k*v*w)*U(xi)+(alpha*lambda+v)*(diff(diff(U(xi), xi), xi)) = 0

 (3)
> 

IM := -2*(diff(diff(U(xi), xi), xi))*v*k-2*U(xi)*k^2*w^2-2*(diff(diff(U(xi), xi), xi))*alpha^2+2*(diff(diff(U(xi), xi), xi))*v^2+(diff(diff(U(xi), xi), xi))*k*w+2*U(xi)^3*k*w-2*U(xi)^3*alpha*beta*k-3*(diff(diff(U(xi), xi), xi))*alpha*k*lambda-U(xi)*k^3*w+2*U(xi)*alpha^2*k^2+U(xi)*alpha*k^3*lambda = 0

-2*(diff(diff(U(xi), xi), xi))*v*k-2*U(xi)*k^2*w^2-2*(diff(diff(U(xi), xi), xi))*alpha^2+2*(diff(diff(U(xi), xi), xi))*v^2+(diff(diff(U(xi), xi), xi))*k*w+2*U(xi)^3*k*w-2*U(xi)^3*alpha*beta*k-3*(diff(diff(U(xi), xi), xi))*alpha*k*lambda-U(xi)*k^3*w+2*U(xi)*alpha^2*k^2+U(xi)*alpha*k^3*lambda = 0

 (4)
> 

collect(%, {U(xi), diff(diff(U(xi), xi), xi)})

(-2*alpha*beta*k+2*k*w)*U(xi)^3+(alpha*k^3*lambda+2*alpha^2*k^2-k^3*w-2*k^2*w^2)*U(xi)+(-3*alpha*k*lambda-2*alpha^2-2*k*v+k*w+2*v^2)*(diff(diff(U(xi), xi), xi)) = 0

 (5)
> 

P := %

(-2*alpha*beta*k+2*k*w)*U(xi)^3+(alpha*k^3*lambda+2*alpha^2*k^2-k^3*w-2*k^2*w^2)*U(xi)+(-3*alpha*k*lambda-2*alpha^2-2*k*v+k*w+2*v^2)*(diff(diff(U(xi), xi), xi)) = 0

 (6)
> 

NULL
> 

NULL
> 

C1 := v = solve(2*v*(1/3)+2*alpha*beta*(1/3) = 0, v)

v = -alpha*beta

 (7)
> 

C2 := k = solve(-3*alpha*k^2*lambda-4*alpha^2*k-k^2*v+2*k^2*w-4*k*v*w = 0, k)

k = (0, -4*(alpha^2+v*w)/(3*alpha*lambda+v-2*w))

 (8)
> 

C22 := subs(C1, C2)

k = (0, -4*(-alpha*beta*w+alpha^2)/(-alpha*beta+3*alpha*lambda-2*w))

 (9)
> 

C222 := k = -(4*(-alpha*beta*w+alpha^2))/(-alpha*beta+3*alpha*lambda-2*w)

k = -4*(-alpha*beta*w+alpha^2)/(-alpha*beta+3*alpha*lambda-2*w)

 (10)
> 

ode := subs({C1, C222}, P)

(8*alpha*beta*(-alpha*beta*w+alpha^2)/(-alpha*beta+3*alpha*lambda-2*w)-8*(-alpha*beta*w+alpha^2)*w/(-alpha*beta+3*alpha*lambda-2*w))*U(xi)^3+(-64*alpha*(-alpha*beta*w+alpha^2)^3*lambda/(-alpha*beta+3*alpha*lambda-2*w)^3+32*alpha^2*(-alpha*beta*w+alpha^2)^2/(-alpha*beta+3*alpha*lambda-2*w)^2+64*(-alpha*beta*w+alpha^2)^3*w/(-alpha*beta+3*alpha*lambda-2*w)^3-32*(-alpha*beta*w+alpha^2)^2*w^2/(-alpha*beta+3*alpha*lambda-2*w)^2)*U(xi)+(12*alpha*(-alpha*beta*w+alpha^2)*lambda/(-alpha*beta+3*alpha*lambda-2*w)-2*alpha^2-8*alpha*beta*(-alpha*beta*w+alpha^2)/(-alpha*beta+3*alpha*lambda-2*w)-4*(-alpha*beta*w+alpha^2)*w/(-alpha*beta+3*alpha*lambda-2*w)+2*alpha^2*beta^2)*(diff(diff(U(xi), xi), xi)) = 0

 (11)
> 

numer(lhs((8*alpha*beta*(-alpha*beta*w+alpha^2)/(-alpha*beta+3*alpha*lambda-2*w)-8*(-alpha*beta*w+alpha^2)*w/(-alpha*beta+3*alpha*lambda-2*w))*U(xi)^3+(-64*alpha*(-alpha*beta*w+alpha^2)^3*lambda/(-alpha*beta+3*alpha*lambda-2*w)^3+32*alpha^2*(-alpha*beta*w+alpha^2)^2/(-alpha*beta+3*alpha*lambda-2*w)^2+64*(-alpha*beta*w+alpha^2)^3*w/(-alpha*beta+3*alpha*lambda-2*w)^3-32*(-alpha*beta*w+alpha^2)^2*w^2/(-alpha*beta+3*alpha*lambda-2*w)^2)*U(xi)+(12*alpha*(-alpha*beta*w+alpha^2)*lambda/(-alpha*beta+3*alpha*lambda-2*w)-2*alpha^2-8*alpha*beta*(-alpha*beta*w+alpha^2)/(-alpha*beta+3*alpha*lambda-2*w)-4*(-alpha*beta*w+alpha^2)*w/(-alpha*beta+3*alpha*lambda-2*w)+2*alpha^2*beta^2)*(diff(diff(U(xi), xi), xi)) = 0))*denom(rhs((8*alpha*beta*(-alpha*beta*w+alpha^2)/(-alpha*beta+3*alpha*lambda-2*w)-8*(-alpha*beta*w+alpha^2)*w/(-alpha*beta+3*alpha*lambda-2*w))*U(xi)^3+(-64*alpha*(-alpha*beta*w+alpha^2)^3*lambda/(-alpha*beta+3*alpha*lambda-2*w)^3+32*alpha^2*(-alpha*beta*w+alpha^2)^2/(-alpha*beta+3*alpha*lambda-2*w)^2+64*(-alpha*beta*w+alpha^2)^3*w/(-alpha*beta+3*alpha*lambda-2*w)^3-32*(-alpha*beta*w+alpha^2)^2*w^2/(-alpha*beta+3*alpha*lambda-2*w)^2)*U(xi)+(12*alpha*(-alpha*beta*w+alpha^2)*lambda/(-alpha*beta+3*alpha*lambda-2*w)-2*alpha^2-8*alpha*beta*(-alpha*beta*w+alpha^2)/(-alpha*beta+3*alpha*lambda-2*w)-4*(-alpha*beta*w+alpha^2)*w/(-alpha*beta+3*alpha*lambda-2*w)+2*alpha^2*beta^2)*(diff(diff(U(xi), xi), xi)) = 0)) = numer(rhs((8*alpha*beta*(-alpha*beta*w+alpha^2)/(-alpha*beta+3*alpha*lambda-2*w)-8*(-alpha*beta*w+alpha^2)*w/(-alpha*beta+3*alpha*lambda-2*w))*U(xi)^3+(-64*alpha*(-alpha*beta*w+alpha^2)^3*lambda/(-alpha*beta+3*alpha*lambda-2*w)^3+32*alpha^2*(-alpha*beta*w+alpha^2)^2/(-alpha*beta+3*alpha*lambda-2*w)^2+64*(-alpha*beta*w+alpha^2)^3*w/(-alpha*beta+3*alpha*lambda-2*w)^3-32*(-alpha*beta*w+alpha^2)^2*w^2/(-alpha*beta+3*alpha*lambda-2*w)^2)*U(xi)+(12*alpha*(-alpha*beta*w+alpha^2)*lambda/(-alpha*beta+3*alpha*lambda-2*w)-2*alpha^2-8*alpha*beta*(-alpha*beta*w+alpha^2)/(-alpha*beta+3*alpha*lambda-2*w)-4*(-alpha*beta*w+alpha^2)*w/(-alpha*beta+3*alpha*lambda-2*w)+2*alpha^2*beta^2)*(diff(diff(U(xi), xi), xi)) = 0))*denom(lhs((8*alpha*beta*(-alpha*beta*w+alpha^2)/(-alpha*beta+3*alpha*lambda-2*w)-8*(-alpha*beta*w+alpha^2)*w/(-alpha*beta+3*alpha*lambda-2*w))*U(xi)^3+(-64*alpha*(-alpha*beta*w+alpha^2)^3*lambda/(-alpha*beta+3*alpha*lambda-2*w)^3+32*alpha^2*(-alpha*beta*w+alpha^2)^2/(-alpha*beta+3*alpha*lambda-2*w)^2+64*(-alpha*beta*w+alpha^2)^3*w/(-alpha*beta+3*alpha*lambda-2*w)^3-32*(-alpha*beta*w+alpha^2)^2*w^2/(-alpha*beta+3*alpha*lambda-2*w)^2)*U(xi)+(12*alpha*(-alpha*beta*w+alpha^2)*lambda/(-alpha*beta+3*alpha*lambda-2*w)-2*alpha^2-8*alpha*beta*(-alpha*beta*w+alpha^2)/(-alpha*beta+3*alpha*lambda-2*w)-4*(-alpha*beta*w+alpha^2)*w/(-alpha*beta+3*alpha*lambda-2*w)+2*alpha^2*beta^2)*(diff(diff(U(xi), xi), xi)) = 0))

-2*alpha*(-24*U(xi)^3*alpha^4*beta^2*lambda+36*U(xi)^3*alpha^4*beta*lambda^2-12*U(xi)^3*alpha^2*beta^3*w^2-16*U(xi)*alpha^4*beta^3*w^2-16*U(xi)*alpha^2*beta^3*w^4+9*(diff(diff(U(xi), xi), xi))*alpha^4*beta^4*lambda-27*(diff(diff(U(xi), xi), xi))*alpha^4*beta^3*lambda^2+27*(diff(diff(U(xi), xi), xi))*alpha^4*beta^2*lambda^3+12*U(xi)^3*alpha^3*beta^2*w-36*U(xi)^3*alpha^3*lambda^2*w+32*U(xi)*alpha^5*beta^2*w+32*U(xi)*alpha^3*beta^2*w^3+32*U(xi)*alpha*beta^2*w^5-2*(diff(diff(U(xi), xi), xi))*alpha^3*beta^4*w+48*U(xi)^3*alpha^2*lambda*w^2-16*U(xi)*alpha^4*beta*w^2-48*U(xi)*alpha^4*lambda*w^2-64*U(xi)*alpha^2*beta*w^4+21*(diff(diff(U(xi), xi), xi))*alpha^4*beta^2*lambda-45*(diff(diff(U(xi), xi), xi))*alpha^4*beta*lambda^2+6*(diff(diff(U(xi), xi), xi))*alpha^2*beta^3*w^2-12*(diff(diff(U(xi), xi), xi))*alpha^3*beta^2*w-36*(diff(diff(U(xi), xi), xi))*alpha^3*lambda^2*w+16*(diff(diff(U(xi), xi), xi))*alpha*beta^2*w^3-12*(diff(diff(U(xi), xi), xi))*alpha^2*beta*w^2+12*(diff(diff(U(xi), xi), xi))*alpha^2*lambda*w^2-4*U(xi)^3*alpha^3*beta^4*w+24*U(xi)^3*alpha^3*beta^3*lambda*w-36*U(xi)^3*alpha^3*beta^2*lambda^2*w+32*U(xi)*alpha^3*beta^3*lambda*w^3+24*U(xi)^3*alpha^2*beta^2*lambda*w^2+36*U(xi)^3*alpha^2*beta*lambda^2*w^2-48*U(xi)*alpha^4*beta^2*lambda*w^2-48*U(xi)*alpha^2*beta^2*lambda*w^4-24*U(xi)^3*alpha^3*beta*lambda*w-48*U(xi)^3*alpha*beta*lambda*w^3+96*U(xi)*alpha^3*beta*lambda*w^3+6*(diff(diff(U(xi), xi), xi))*alpha^3*beta^3*lambda*w+18*(diff(diff(U(xi), xi), xi))*alpha^3*beta^2*lambda^2*w-54*(diff(diff(U(xi), xi), xi))*alpha^3*beta*lambda^3*w-48*(diff(diff(U(xi), xi), xi))*alpha^2*beta^2*lambda*w^2+90*(diff(diff(U(xi), xi), xi))*alpha^2*beta*lambda^2*w^2+48*(diff(diff(U(xi), xi), xi))*alpha^3*beta*lambda*w-48*(diff(diff(U(xi), xi), xi))*alpha*beta*lambda*w^3+4*U(xi)^3*alpha^4*beta^3-(diff(diff(U(xi), xi), xi))*alpha^4*beta^5+16*U(xi)^3*beta*w^4-16*U(xi)*alpha^6*beta+16*U(xi)*alpha^6*lambda-3*(diff(diff(U(xi), xi), xi))*alpha^4*beta^3+27*(diff(diff(U(xi), xi), xi))*alpha^4*lambda^3-16*U(xi)^3*alpha*w^3+32*U(xi)*alpha^3*w^3+8*(diff(diff(U(xi), xi), xi))*beta*w^4) = 0

 (12)
> 

simplify(-2*alpha*(24*U(xi)^3*alpha^3*beta^3*lambda*w-36*U(xi)^3*alpha^3*beta^2*lambda^2*w+32*U(xi)*alpha^3*beta^3*lambda*w^3+24*U(xi)^3*alpha^2*beta^2*lambda*w^2+36*U(xi)^3*alpha^2*beta*lambda^2*w^2-48*U(xi)*alpha^4*beta^2*lambda*w^2-48*U(xi)*alpha^2*beta^2*lambda*w^4-24*U(xi)^3*alpha^3*beta*lambda*w-48*U(xi)^3*alpha*beta*lambda*w^3+96*U(xi)*alpha^3*beta*lambda*w^3+6*(diff(diff(U(xi), xi), xi))*alpha^3*beta^3*lambda*w+18*(diff(diff(U(xi), xi), xi))*alpha^3*beta^2*lambda^2*w-54*(diff(diff(U(xi), xi), xi))*alpha^3*beta*lambda^3*w-48*(diff(diff(U(xi), xi), xi))*alpha^2*beta^2*lambda*w^2+90*(diff(diff(U(xi), xi), xi))*alpha^2*beta*lambda^2*w^2+48*(diff(diff(U(xi), xi), xi))*alpha^3*beta*lambda*w-48*(diff(diff(U(xi), xi), xi))*alpha*beta*lambda*w^3-24*U(xi)^3*alpha^4*beta^2*lambda+36*U(xi)^3*alpha^4*beta*lambda^2-12*U(xi)^3*alpha^2*beta^3*w^2-16*U(xi)*alpha^4*beta^3*w^2-16*U(xi)*alpha^2*beta^3*w^4+9*(diff(diff(U(xi), xi), xi))*alpha^4*beta^4*lambda-27*(diff(diff(U(xi), xi), xi))*alpha^4*beta^3*lambda^2+27*(diff(diff(U(xi), xi), xi))*alpha^4*beta^2*lambda^3+12*U(xi)^3*alpha^3*beta^2*w-36*U(xi)^3*alpha^3*lambda^2*w+32*U(xi)*alpha^5*beta^2*w+32*U(xi)*alpha^3*beta^2*w^3+32*U(xi)*alpha*beta^2*w^5-2*(diff(diff(U(xi), xi), xi))*alpha^3*beta^4*w+48*U(xi)^3*alpha^2*lambda*w^2-16*U(xi)*alpha^4*beta*w^2-48*U(xi)*alpha^4*lambda*w^2-64*U(xi)*alpha^2*beta*w^4+21*(diff(diff(U(xi), xi), xi))*alpha^4*beta^2*lambda-45*(diff(diff(U(xi), xi), xi))*alpha^4*beta*lambda^2+6*(diff(diff(U(xi), xi), xi))*alpha^2*beta^3*w^2-12*(diff(diff(U(xi), xi), xi))*alpha^3*beta^2*w-36*(diff(diff(U(xi), xi), xi))*alpha^3*lambda^2*w+16*(diff(diff(U(xi), xi), xi))*alpha*beta^2*w^3-12*(diff(diff(U(xi), xi), xi))*alpha^2*beta*w^2+12*(diff(diff(U(xi), xi), xi))*alpha^2*lambda*w^2-4*U(xi)^3*alpha^3*beta^4*w-(diff(diff(U(xi), xi), xi))*alpha^4*beta^5+4*U(xi)^3*alpha^4*beta^3+16*U(xi)^3*beta*w^4-16*U(xi)*alpha^6*beta+16*U(xi)*alpha^6*lambda-3*(diff(diff(U(xi), xi), xi))*alpha^4*beta^3+27*(diff(diff(U(xi), xi), xi))*alpha^4*lambda^3-16*U(xi)^3*alpha*w^3+32*U(xi)*alpha^3*w^3+8*(diff(diff(U(xi), xi), xi))*beta*w^4) = 0)

-64*alpha*((1/4)*((1/2)*(-beta^3+3*beta^2*lambda-3*beta+3*lambda)*alpha^2+beta*w*(beta-3*lambda)*alpha+beta*w^2)*((1/2)*(beta-3*lambda)*alpha+w)^2*(diff(diff(U(xi), xi), xi))+((1/2)*(-alpha*beta+w)*((1/2)*(beta-3*lambda)*alpha+w)^2*U(xi)^2+alpha*((1/2)*(-beta+lambda)*alpha^3+w*beta*alpha^2*lambda-(1/2)*w^2*(beta+3*lambda)*alpha+w^3)*(beta*w-alpha))*(beta*w-alpha)*U(xi)) = 0

 (13)
> 

%/(-64*alpha)

(1/4)*((1/2)*(-beta^3+3*beta^2*lambda-3*beta+3*lambda)*alpha^2+beta*w*(beta-3*lambda)*alpha+beta*w^2)*((1/2)*(beta-3*lambda)*alpha+w)^2*(diff(diff(U(xi), xi), xi))+((1/2)*(-alpha*beta+w)*((1/2)*(beta-3*lambda)*alpha+w)^2*U(xi)^2+alpha*((1/2)*(-beta+lambda)*alpha^3+w*beta*alpha^2*lambda-(1/2)*w^2*(beta+3*lambda)*alpha+w^3)*(beta*w-alpha))*(beta*w-alpha)*U(xi) = 0

 (14)
> 

PP := numer(lhs((1/4)*((1/2)*(-beta^3+3*beta^2*lambda-3*beta+3*lambda)*alpha^2+beta*w*(beta-3*lambda)*alpha+beta*w^2)*((1/2)*(beta-3*lambda)*alpha+w)^2*(diff(diff(U(xi), xi), xi))+((1/2)*(-alpha*beta+w)*((1/2)*(beta-3*lambda)*alpha+w)^2*U(xi)^2+alpha*((1/2)*(-beta+lambda)*alpha^3+w*beta*alpha^2*lambda-(1/2)*w^2*(beta+3*lambda)*alpha+w^3)*(beta*w-alpha))*(beta*w-alpha)*U(xi) = 0))*denom(rhs((1/4)*((1/2)*(-beta^3+3*beta^2*lambda-3*beta+3*lambda)*alpha^2+beta*w*(beta-3*lambda)*alpha+beta*w^2)*((1/2)*(beta-3*lambda)*alpha+w)^2*(diff(diff(U(xi), xi), xi))+((1/2)*(-alpha*beta+w)*((1/2)*(beta-3*lambda)*alpha+w)^2*U(xi)^2+alpha*((1/2)*(-beta+lambda)*alpha^3+w*beta*alpha^2*lambda-(1/2)*w^2*(beta+3*lambda)*alpha+w^3)*(beta*w-alpha))*(beta*w-alpha)*U(xi) = 0)) = numer(rhs((1/4)*((1/2)*(-beta^3+3*beta^2*lambda-3*beta+3*lambda)*alpha^2+beta*w*(beta-3*lambda)*alpha+beta*w^2)*((1/2)*(beta-3*lambda)*alpha+w)^2*(diff(diff(U(xi), xi), xi))+((1/2)*(-alpha*beta+w)*((1/2)*(beta-3*lambda)*alpha+w)^2*U(xi)^2+alpha*((1/2)*(-beta+lambda)*alpha^3+w*beta*alpha^2*lambda-(1/2)*w^2*(beta+3*lambda)*alpha+w^3)*(beta*w-alpha))*(beta*w-alpha)*U(xi) = 0))*denom(lhs((1/4)*((1/2)*(-beta^3+3*beta^2*lambda-3*beta+3*lambda)*alpha^2+beta*w*(beta-3*lambda)*alpha+beta*w^2)*((1/2)*(beta-3*lambda)*alpha+w)^2*(diff(diff(U(xi), xi), xi))+((1/2)*(-alpha*beta+w)*((1/2)*(beta-3*lambda)*alpha+w)^2*U(xi)^2+alpha*((1/2)*(-beta+lambda)*alpha^3+w*beta*alpha^2*lambda-(1/2)*w^2*(beta+3*lambda)*alpha+w^3)*(beta*w-alpha))*(beta*w-alpha)*U(xi) = 0))

-24*U(xi)^3*alpha^4*beta^2*lambda+36*U(xi)^3*alpha^4*beta*lambda^2-12*U(xi)^3*alpha^2*beta^3*w^2-16*U(xi)*alpha^4*beta^3*w^2-16*U(xi)*alpha^2*beta^3*w^4+9*(diff(diff(U(xi), xi), xi))*alpha^4*beta^4*lambda-27*(diff(diff(U(xi), xi), xi))*alpha^4*beta^3*lambda^2+27*(diff(diff(U(xi), xi), xi))*alpha^4*beta^2*lambda^3+12*U(xi)^3*alpha^3*beta^2*w-36*U(xi)^3*alpha^3*lambda^2*w+32*U(xi)*alpha^5*beta^2*w+32*U(xi)*alpha^3*beta^2*w^3+32*U(xi)*alpha*beta^2*w^5-2*(diff(diff(U(xi), xi), xi))*alpha^3*beta^4*w+48*U(xi)^3*alpha^2*lambda*w^2-16*U(xi)*alpha^4*beta*w^2-48*U(xi)*alpha^4*lambda*w^2-64*U(xi)*alpha^2*beta*w^4+21*(diff(diff(U(xi), xi), xi))*alpha^4*beta^2*lambda-45*(diff(diff(U(xi), xi), xi))*alpha^4*beta*lambda^2+6*(diff(diff(U(xi), xi), xi))*alpha^2*beta^3*w^2-12*(diff(diff(U(xi), xi), xi))*alpha^3*beta^2*w-36*(diff(diff(U(xi), xi), xi))*alpha^3*lambda^2*w+16*(diff(diff(U(xi), xi), xi))*alpha*beta^2*w^3-12*(diff(diff(U(xi), xi), xi))*alpha^2*beta*w^2+12*(diff(diff(U(xi), xi), xi))*alpha^2*lambda*w^2-4*U(xi)^3*alpha^3*beta^4*w+24*U(xi)^3*alpha^3*beta^3*lambda*w-36*U(xi)^3*alpha^3*beta^2*lambda^2*w+32*U(xi)*alpha^3*beta^3*lambda*w^3+24*U(xi)^3*alpha^2*beta^2*lambda*w^2+36*U(xi)^3*alpha^2*beta*lambda^2*w^2-48*U(xi)*alpha^4*beta^2*lambda*w^2-48*U(xi)*alpha^2*beta^2*lambda*w^4-24*U(xi)^3*alpha^3*beta*lambda*w-48*U(xi)^3*alpha*beta*lambda*w^3+96*U(xi)*alpha^3*beta*lambda*w^3+6*(diff(diff(U(xi), xi), xi))*alpha^3*beta^3*lambda*w+18*(diff(diff(U(xi), xi), xi))*alpha^3*beta^2*lambda^2*w-54*(diff(diff(U(xi), xi), xi))*alpha^3*beta*lambda^3*w-48*(diff(diff(U(xi), xi), xi))*alpha^2*beta^2*lambda*w^2+90*(diff(diff(U(xi), xi), xi))*alpha^2*beta*lambda^2*w^2+48*(diff(diff(U(xi), xi), xi))*alpha^3*beta*lambda*w-48*(diff(diff(U(xi), xi), xi))*alpha*beta*lambda*w^3+4*U(xi)^3*alpha^4*beta^3-(diff(diff(U(xi), xi), xi))*alpha^4*beta^5+16*U(xi)^3*beta*w^4-16*U(xi)*alpha^6*beta+16*U(xi)*alpha^6*lambda-3*(diff(diff(U(xi), xi), xi))*alpha^4*beta^3+27*(diff(diff(U(xi), xi), xi))*alpha^4*lambda^3-16*U(xi)^3*alpha*w^3+32*U(xi)*alpha^3*w^3+8*(diff(diff(U(xi), xi), xi))*beta*w^4 = 0

 (15)
> 

NULL
> 

collect(PP, {U(xi), diff(U(xi), xi), diff(diff(U(xi), xi), xi)})

(-4*alpha^3*beta^4*w+24*alpha^3*beta^3*lambda*w-36*alpha^3*beta^2*lambda^2*w+4*alpha^4*beta^3-24*alpha^4*beta^2*lambda+36*alpha^4*beta*lambda^2-12*alpha^2*beta^3*w^2+24*alpha^2*beta^2*lambda*w^2+36*alpha^2*beta*lambda^2*w^2+12*alpha^3*beta^2*w-24*alpha^3*beta*lambda*w-36*alpha^3*lambda^2*w-48*alpha*beta*lambda*w^3+48*alpha^2*lambda*w^2+16*beta*w^4-16*alpha*w^3)*U(xi)^3+(32*alpha^3*beta^3*lambda*w^3-16*alpha^4*beta^3*w^2-48*alpha^4*beta^2*lambda*w^2-16*alpha^2*beta^3*w^4-48*alpha^2*beta^2*lambda*w^4+32*alpha^5*beta^2*w+32*alpha^3*beta^2*w^3+96*alpha^3*beta*lambda*w^3+32*alpha*beta^2*w^5-16*alpha^6*beta+16*alpha^6*lambda-16*alpha^4*beta*w^2-48*alpha^4*lambda*w^2-64*alpha^2*beta*w^4+32*alpha^3*w^3)*U(xi)+(-alpha^4*beta^5+9*alpha^4*beta^4*lambda-27*alpha^4*beta^3*lambda^2+27*alpha^4*beta^2*lambda^3-2*alpha^3*beta^4*w+6*alpha^3*beta^3*lambda*w+18*alpha^3*beta^2*lambda^2*w-54*alpha^3*beta*lambda^3*w-3*alpha^4*beta^3+21*alpha^4*beta^2*lambda-45*alpha^4*beta*lambda^2+27*alpha^4*lambda^3+6*alpha^2*beta^3*w^2-48*alpha^2*beta^2*lambda*w^2+90*alpha^2*beta*lambda^2*w^2-12*alpha^3*beta^2*w+48*alpha^3*beta*lambda*w-36*alpha^3*lambda^2*w+16*alpha*beta^2*w^3-48*alpha*beta*lambda*w^3-12*alpha^2*beta*w^2+12*alpha^2*lambda*w^2+8*beta*w^4)*(diff(diff(U(xi), xi), xi)) = 0

 (16)
 

NULL

Download B-R.mw

Simplifying nonlinear terms differential equation...

Asked by: salim-barzani 1410
simplification differential-equations duplicate-question
May 06 2025
3  1

How can we eliminate nonlinear terms involving two functions in a differential equation?

> 

restart
> 

with(PDEtools)
> 

with(LinearAlgebra)
> 

NULL
> 

with(SolveTools)
> 

undeclare(prime)

`There is no more prime differentiation variable; all derivatives will be displayed as indexed functions`

 (1)
> 

declare(G(xi)); declare(Q(x, t)); declare(Q1(x, t))

G(xi)*`will now be displayed as`*G

  

Q(x, t)*`will now be displayed as`*Q

  

Q1(x, t)*`will now be displayed as`*Q1

 (2)
> 

NULL
> 

q := (sqrt(P)+Q(x, t))*exp(I*gamma*P*t); B := (sqrt(P)+Q(x, t))*exp(-I*gamma*P*t); B1 := sqrt(P)+Q(x, t); P+sqrt(P)*(Q1(x, t)+Q(x, t))
> 

GeF := I*(diff(q, t))+alpha[1]*(diff(q, x, x))+alpha[2]*(P+sqrt(P)*(Q1(x, t)+Q(x, t)))*q+alpha[3]*(P+sqrt(P)*(Q1(x, t)+Q(x, t)))^2*q+alpha[4]*(P+sqrt(P)*(Q1(x, t)+Q(x, t)))^3*q+alpha[5]*(diff(P+sqrt(P)*(Q1(x, t)+Q(x, t)), x, x))*q = 0
> 

K := simplify(GeF*exp(-I*gamma*P*t))

(Q(x, t)^4*alpha[4]+3*Q(x, t)^3*Q1(x, t)*alpha[4]+3*(Q1(x, t)^2*alpha[4]+alpha[3])*Q(x, t)^2+Q1(x, t)*(Q1(x, t)^2*alpha[4]+4*alpha[3])*Q(x, t)+Q1(x, t)^2*alpha[3]+alpha[2]-gamma)*P^(3/2)+(6*Q(x, t)^2*alpha[4]+9*Q(x, t)*Q1(x, t)*alpha[4]+3*Q1(x, t)^2*alpha[4]+alpha[3])*P^(5/2)+(P^(1/2)*Q(x, t)*alpha[5]+P*alpha[5]+alpha[1])*(diff(diff(Q(x, t), x), x))+alpha[5]*(P^(1/2)*Q(x, t)+P)*(diff(diff(Q1(x, t), x), x))+P^(7/2)*alpha[4]+I*(diff(Q(x, t), t))+alpha[2]*(Q1(x, t)*Q(x, t)+Q(x, t)^2)*P^(1/2)+(4*P^2*alpha[4]+P*alpha[3])*Q(x, t)^3+(9*P^2*alpha[4]+2*P*alpha[3])*Q1(x, t)*Q(x, t)^2+((6*P^2*alpha[4]+P*alpha[3])*Q1(x, t)^2+4*alpha[4]*P^3+3*alpha[3]*P^2+(2*alpha[2]-gamma)*P)*Q(x, t)+P^2*Q1(x, t)^3*alpha[4]+(3*P^3*alpha[4]+2*P^2*alpha[3]+P*alpha[2])*Q1(x, t) = 0

 (3)
> 

remove(has, K, {Q(x, t)^2, Q(x, t)^3, Q(x, t)^4, Q1(x, t)^2, Q1(x, t)^3, Q1(x, t)^4})

() = 0

 (4)
> 

NULL
> 

NULL
> 

AA := (alpha[2]-gamma)*P^(3/2)+alpha[3]*P^(5/2)+(P*alpha[5]+alpha[1])*(diff(Q(x, t), x, x))+alpha[5]*P*(diff(Q1(x, t), x, x))+P^(7/2)*alpha[4]+I*(diff(Q(x, t), t))+(4*alpha[4]*P^3+3*alpha[3]*P^2+(2*alpha[2]-gamma)*P)*Q(x, t)+(3*P^3*alpha[4]+2*P^2*alpha[3]+P*alpha[2])*Q1(x, t) = 0

(alpha[2]-gamma)*P^(3/2)+P^(5/2)*alpha[3]+(P*alpha[5]+alpha[1])*(diff(diff(Q(x, t), x), x))+P*(diff(diff(Q1(x, t), x), x))*alpha[5]+P^(7/2)*alpha[4]+I*(diff(Q(x, t), t))+(4*alpha[4]*P^3+3*alpha[3]*P^2+(2*alpha[2]-gamma)*P)*Q(x, t)+(3*P^3*alpha[4]+2*P^2*alpha[3]+P*alpha[2])*Q1(x, t) = 0

 (5)
 
> 

test := (alpha[2]-gamma)*P^(3/2)+alpha[3]*P^(5/2)+(P*alpha[5]+alpha[1])*0+P*alpha[5]*0+P^(7/2)*alpha[4]+I*0 = 0

(alpha[2]-gamma)*P^(3/2)+P^(5/2)*alpha[3]+P^(7/2)*alpha[4] = 0

 (6)
 

NULL

Download remove.mw

1 2 3 4 5 6 7 Last Page 1 of 40