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salim-barzani

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1 years, 19 days
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salim-barzani 1560
January 01 2025
0 0

@mmcdara  also don't find all parameter becuase in this ode part we have condition i founded before but becuase is not neccesary i didn't mentioned please just find thus parameter in paper mentioned V and sigma are condition i found it  in first part which i transfrom the PDE to ODE i get it from imaginary part  so i don't want make confusing for you becuase of this i didn't but i will mention the condition 

condition.mw

reply...

salim-barzani 1560
January 01 2025
0 0

@mmcdara  i want do the same like paper did factoring (m+F)=(m+G'/G) 

reply...

salim-barzani 1560
December 31 2024
0 0

@mmcdara 

Previously, you solved a problem for me involving an equation like (m+1/G′)=ϕ. Your explanation was excellent, and I enjoyed learning the new method you used to solve it. Inspired by that, I attempted to apply the same technique to factor (m+G′G)=phi, but I couldn't figure it out this time.

I don’t fully understand the technique you demonstrated earlier, but I’d really appreciate it if you could explain it again. If possible, could you also provide a code implementation for this problem? Your previous explanation was incredibly clear and helpful. Thank you!

Thanks, you did a great job...

salim-barzani 1560
December 30 2024
0 0

@nm that is 2 day i am stuck becuase of this my second odetest  make  a problem i knew problem is parameter becuase in a lot place have a gamma  anyway thank you so much is great it is work .

thank you so much...

salim-barzani 1560
December 30 2024
0 0

@Oliver K  but union not work but try the identical is work.

don't use chatGpt...

salim-barzani 1560
December 30 2024
0 0

@janhardo  i want figure out by maple.

add some more detail to question post...

salim-barzani 1560
December 29 2024
0 0

@dharr if you watch the file part in indet we have name but i remove the name instead i write down the parameter but it say is not exists how this is possible

How about upload code...

salim-barzani 1560
December 29 2024
0 0

@dharr it is easy to find all case really is a good code  @ mmcdara write the code i asked letter  for change to arbitrary parameter but he didn't response ,becuase i think  my PDE is not going to zero becuase all parameter there must be a problem i should found i am stuck becuase my pde which i transformed to ode is not going to zero have a problem with parameter but i don't know what is it no one answered untill now i think thus parameter make a problem

A secret...

salim-barzani 1560
December 29 2024
0 0

@janhardo have a long story 

if have any other question ask...

salim-barzani 1560
December 29 2024
0 0

@nm  i try to explain in this file 


 

> 

restart
> 

with(PDEtools)
> 

with(LinearAlgebra)
> 

with(Physics)
> 

with(SolveTools)
> 

undeclare(prime)

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

 (1)
> 

_local(gamma)

Warning, A new binding for the name `gamma` has been created. The global instance of this name is still accessible using the :- prefix, :-`gamma`.  See ?protect for details.

  
> 

declare(Omega(x, t)); declare(U(xi)); declare(u(x, y, z, t)); declare(Q(xi)); declare(V(xi))

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

  

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

  

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

  

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

  

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

 (2)
> 

pde1 := I*(diff(Omega(x, t)^m, t))+alpha*(diff(Omega(x, t)^m, `$`(x, 2)))+I*beta*(diff(abs(Omega(x, t))^(2*n)*Omega(x, t)^m, x))+m*sigma*Omega(x, t)^m*(diff(W(t), t)) = I*gamma*abs(Omega(x, t))^(2*n)*(diff(Omega(x, t)^m, x))+delta*abs(Omega(x, t))^(4*n)*Omega(x, t)^m

I*Omega(x, t)^m*m*(diff(Omega(x, t), t))/Omega(x, t)+alpha*(Omega(x, t)^m*m^2*(diff(Omega(x, t), x))^2/Omega(x, t)^2+Omega(x, t)^m*m*(diff(diff(Omega(x, t), x), x))/Omega(x, t)-Omega(x, t)^m*m*(diff(Omega(x, t), x))^2/Omega(x, t)^2)+I*beta*(abs(Omega(x, t))^(2*n)*n*((diff(Omega(x, t), x))*conjugate(Omega(x, t))+Omega(x, t)*(diff(conjugate(Omega(x, t)), x)))*Omega(x, t)^m/abs(Omega(x, t))^2+abs(Omega(x, t))^(2*n)*Omega(x, t)^m*m*(diff(Omega(x, t), x))/Omega(x, t))+m*sigma*Omega(x, t)^m*(diff(W(t), t)) = I*gamma*abs(Omega(x, t))^(2*n)*Omega(x, t)^m*m*(diff(Omega(x, t), x))/Omega(x, t)+delta*abs(Omega(x, t))^(4*n)*Omega(x, t)^m

 (3)
> 

NULL
> 

ode := 4*V(xi)^4*n^2*sigma+(-4*beta*k*m*n^2+4*gamma*k*m*n^2)*V(xi)^3+(4*alpha*k^2*m^2*n^2-4*delta^2*m*n^2+4*m*n^2*w)*V(xi)^2-2*V(xi)*(diff(diff(V(xi), xi), xi))*alpha*m*n+(-alpha*m^2+2*alpha*m*n)*(diff(V(xi), xi))^2 = 0

4*V(xi)^4*n^2*sigma+(-4*beta*k*m*n^2+4*gamma*k*m*n^2)*V(xi)^3+(4*alpha*k^2*m^2*n^2-4*delta^2*m*n^2+4*m*n^2*w)*V(xi)^2-2*V(xi)*(diff(diff(V(xi), xi), xi))*alpha*m*n+(-alpha*m^2+2*alpha*m*n)*(diff(V(xi), xi))^2 = 0

 (4)
> 

L := Omega(x, t) = U(xi)*exp(I*(-k*(tau*c[0]+xi)+w*tau+delta*W(tau)-delta^2*tau))

Omega(x, t) = U(xi)*exp(I*(-k*(tau*c[0]+xi)+w*tau+delta*W(tau)-delta^2*tau))

 (5)
> 

T := U(xi) = V(xi)^(1/(2*n))

U(xi) = V(xi)^((1/2)/n)

 (6)
> 

NULL
> 

ode1 := U(xi)^3*U(xi)^(-1+2*n)*beta*k*m-U(xi)^2*gamma*U(xi)^(2*n)*k*m+U(xi)^2*delta^2*m+I*U(xi)^2*(diff(U(xi), xi))*U(xi)^(-1+2*n)*beta*m-I*U(xi)*(diff(U(xi), xi))*gamma*U(xi)^(2*n)*m-(2*I)*U(xi)*(diff(U(xi), xi))*alpha*k*m^2-U(xi)^2*alpha*k^2*m^2-U(xi)^2*m*w-I*U(xi)*(diff(U(xi), xi))*m*c[0]+(2*I)*U(xi)^2*(diff(U(xi), xi))*U(xi)^(-1+2*n)*beta*n+(diff(U(xi), xi))^2*alpha*m^2-sigma*U(xi)^(4*n)*U(xi)^2+U(xi)*(diff(diff(U(xi), xi), xi))*alpha*m-(diff(U(xi), xi))^2*alpha*m = 0

U(xi)^3*U(xi)^(-1+2*n)*beta*k*m-U(xi)^2*gamma*U(xi)^(2*n)*k*m+U(xi)^2*delta^2*m+I*U(xi)^2*(diff(U(xi), xi))*U(xi)^(-1+2*n)*beta*m-I*U(xi)*(diff(U(xi), xi))*gamma*U(xi)^(2*n)*m-(2*I)*U(xi)*(diff(U(xi), xi))*alpha*k*m^2-U(xi)^2*alpha*k^2*m^2-U(xi)^2*m*w-I*U(xi)*(diff(U(xi), xi))*m*c[0]+(2*I)*U(xi)^2*(diff(U(xi), xi))*U(xi)^(-1+2*n)*beta*n+(diff(U(xi), xi))^2*alpha*m^2-sigma*U(xi)^(4*n)*U(xi)^2+U(xi)*(diff(diff(U(xi), xi), xi))*alpha*m-(diff(U(xi), xi))^2*alpha*m = 0

 (7)
> 

S := diff(G(xi), `$`(xi, 2))+(2*m*mu+lambda)*(diff(G(xi), xi))+mu = 0

diff(diff(G(xi), xi), xi)+(2*m*mu+lambda)*(diff(G(xi), xi))+mu = 0

 (8)
> 

S1 := dsolve(S, G(xi))

G(xi) = -exp(-(2*m*mu+lambda)*xi)*c__1/(2*m*mu+lambda)-mu*xi/(2*m*mu+lambda)+c__2

 (9)
> 

S2 := diff(G(xi) = -exp(-(2*m*mu+lambda)*xi)*c__1/(2*m*mu+lambda)-mu*xi/(2*m*mu+lambda)+c__2, xi)

diff(G(xi), xi) = -(-2*m*mu-lambda)*exp(-(2*m*mu+lambda)*xi)*c__1/(2*m*mu+lambda)-mu/(2*m*mu+lambda)

 (10)
> 

K := V(xi) = a[-1]/(m+1/(diff(G(xi), xi)))+a[0]+a[1]*(m+1/(diff(G(xi), xi)))

V(xi) = a[-1]/(m+1/(diff(G(xi), xi)))+a[0]+a[1]*(m+1/(diff(G(xi), xi)))

 (11)
> 

case1 := {alpha = alpha, beta = gamma, delta = delta, gamma = gamma, k = k, lambda = 0, m = 2*n, mu = mu, n = n, sigma = 32*alpha*mu^2*n^4/a[-1]^2, w = -2*alpha*k^2*n-4*alpha*mu^2*n+delta^2, a[-1] = a[-1], a[0] = 0, a[1] = 0}

{alpha = alpha, beta = gamma, delta = delta, gamma = gamma, k = k, lambda = 0, m = 2*n, mu = mu, n = n, sigma = 32*alpha*mu^2*n^4/a[-1]^2, w = -2*alpha*k^2*n-4*alpha*mu^2*n+delta^2, a[-1] = a[-1], a[0] = 0, a[1] = 0}

 (12)
> 

F1 := subs(case1, K)

V(xi) = a[-1]/(2*n+1/(diff(G(xi), xi)))

 (13)
> 

F2 := subs(case1, ode)

128*V(xi)^4*n^6*alpha*mu^2/a[-1]^2+(16*alpha*k^2*n^4-8*delta^2*n^3+8*n^3*(-2*alpha*k^2*n-4*alpha*mu^2*n+delta^2))*V(xi)^2-4*V(xi)*(diff(diff(V(xi), xi), xi))*alpha*n^2 = 0

 (14)

``

 (15)
> 

W1 := subs(S2, F1)

V(xi) = a[-1]/(2*n+1/(-(-2*m*mu-lambda)*exp(-(2*m*mu+lambda)*xi)*c__1/(2*m*mu+lambda)-mu/(2*m*mu+lambda)))

 (16)
> 

W2 := subs(case1, W1)

V(xi) = a[-1]/(2*n+1/(exp(-4*mu*n*xi)*c__1-(1/4)/n))

 (17)
> 

odetest(W2, F2)

0

 (18)
> 

NULL
> 

NULL
> 

T2 := subs(W2, T)

U(xi) = (a[-1]/(2*n+1/(exp(-4*mu*n*xi)*c__1-(1/4)/n)))^((1/2)/n)

 (19)
> 

T3 := subs(T2, L)

Omega(x, t) = (a[-1]/(2*n+1/(exp(-4*mu*n*xi)*c__1-(1/4)/n)))^((1/2)/n)*exp(I*(-k*(tau*c[0]+xi)+w*tau+delta*W(tau)-delta^2*tau))

 (20)
> 

condition1 := c[0] = -2*alpha*k*m; condition2 := beta = gamma*m/(m+2*n)

c[0] = -2*alpha*k*m

  

beta = gamma*m/(m+2*n)

 (21)
> 

n := 2; M := 1

2

  

1

 (22)
> 

P := subs(case1, ode1)

4*U(xi)^2*delta^2-(32*I)*U(xi)*(diff(U(xi), xi))*alpha*k-16*U(xi)^2*alpha*k^2-4*U(xi)^2*(-4*alpha*k^2-8*alpha*mu^2+delta^2)-(4*I)*U(xi)*(diff(U(xi), xi))*c[0]+(4*I)*U(xi)^5*(diff(U(xi), xi))*gamma+12*(diff(U(xi), xi))^2*alpha-512*alpha*mu^2*U(xi)^10/a[-1]^2+4*U(xi)*(diff(diff(U(xi), xi), xi))*alpha = 0

 (23)
> 

P1 := subs(case1, T2)

U(xi) = (a[-1]/(4+1/(exp(-8*mu*xi)*c__1-1/8)))^(1/4)

 (24)
> 

Pe := odetest(P1, P)

-(512*I)*mu*c__1*(8*c__1*a[-1]/(exp(8*mu*xi)+8*c__1)-a[-1]*exp(8*mu*xi)/(exp(8*mu*xi)+8*c__1))^(1/2)*exp(16*mu*xi)*alpha*k/((exp(8*mu*xi)-8*c__1)*(exp(8*mu*xi)+8*c__1)^2)-(16*I)*mu*c__1*(8*c__1*a[-1]/(exp(8*mu*xi)+8*c__1)-a[-1]*exp(8*mu*xi)/(exp(8*mu*xi)+8*c__1))^(1/2)*exp(16*mu*xi)*gamma*a[-1]/((exp(8*mu*xi)-8*c__1)*(exp(8*mu*xi)+8*c__1)^2)-(4096*I)*mu*c__1^2*(8*c__1*a[-1]/(exp(8*mu*xi)+8*c__1)-a[-1]*exp(8*mu*xi)/(exp(8*mu*xi)+8*c__1))^(1/2)*exp(8*mu*xi)*alpha*k/((exp(8*mu*xi)-8*c__1)*(exp(8*mu*xi)+8*c__1)^2)+(128*I)*mu*c__1^2*(8*c__1*a[-1]/(exp(8*mu*xi)+8*c__1)-a[-1]*exp(8*mu*xi)/(exp(8*mu*xi)+8*c__1))^(1/2)*exp(8*mu*xi)*gamma*a[-1]/((exp(8*mu*xi)-8*c__1)*(exp(8*mu*xi)+8*c__1)^2)-(64*I)*mu*c__1*(8*c__1*a[-1]/(exp(8*mu*xi)+8*c__1)-a[-1]*exp(8*mu*xi)/(exp(8*mu*xi)+8*c__1))^(1/2)*exp(16*mu*xi)*c[0]/((exp(8*mu*xi)-8*c__1)*(exp(8*mu*xi)+8*c__1)^2)-(512*I)*mu*c__1^2*(8*c__1*a[-1]/(exp(8*mu*xi)+8*c__1)-a[-1]*exp(8*mu*xi)/(exp(8*mu*xi)+8*c__1))^(1/2)*exp(8*mu*xi)*c[0]/((exp(8*mu*xi)-8*c__1)*(exp(8*mu*xi)+8*c__1)^2)

 (25)
> 

subs({condition1, condition2}, Pe)

-(512*I)*mu*c__1*(8*c__1*a[-1]/(exp(8*mu*xi)+8*c__1)-a[-1]*exp(8*mu*xi)/(exp(8*mu*xi)+8*c__1))^(1/2)*exp(16*mu*xi)*alpha*k/((exp(8*mu*xi)-8*c__1)*(exp(8*mu*xi)+8*c__1)^2)-(16*I)*mu*c__1*(8*c__1*a[-1]/(exp(8*mu*xi)+8*c__1)-a[-1]*exp(8*mu*xi)/(exp(8*mu*xi)+8*c__1))^(1/2)*exp(16*mu*xi)*gamma*a[-1]/((exp(8*mu*xi)-8*c__1)*(exp(8*mu*xi)+8*c__1)^2)-(4096*I)*mu*c__1^2*(8*c__1*a[-1]/(exp(8*mu*xi)+8*c__1)-a[-1]*exp(8*mu*xi)/(exp(8*mu*xi)+8*c__1))^(1/2)*exp(8*mu*xi)*alpha*k/((exp(8*mu*xi)-8*c__1)*(exp(8*mu*xi)+8*c__1)^2)+(128*I)*mu*c__1^2*(8*c__1*a[-1]/(exp(8*mu*xi)+8*c__1)-a[-1]*exp(8*mu*xi)/(exp(8*mu*xi)+8*c__1))^(1/2)*exp(8*mu*xi)*gamma*a[-1]/((exp(8*mu*xi)-8*c__1)*(exp(8*mu*xi)+8*c__1)^2)+(128*I)*mu*c__1*(8*c__1*a[-1]/(exp(8*mu*xi)+8*c__1)-a[-1]*exp(8*mu*xi)/(exp(8*mu*xi)+8*c__1))^(1/2)*exp(16*mu*xi)*alpha*k*m/((exp(8*mu*xi)-8*c__1)*(exp(8*mu*xi)+8*c__1)^2)+(1024*I)*mu*c__1^2*(8*c__1*a[-1]/(exp(8*mu*xi)+8*c__1)-a[-1]*exp(8*mu*xi)/(exp(8*mu*xi)+8*c__1))^(1/2)*exp(8*mu*xi)*alpha*k*m/((exp(8*mu*xi)-8*c__1)*(exp(8*mu*xi)+8*c__1)^2)

 (26)
> 

NULL
> 

NULL

NULL


 

Download explain.mw

a question?...

salim-barzani 1560
December 28 2024
0 0

@mmcdara  in the code i don't want all parameter maybe 4 or 5 is enough How i do that?

F-P.mw

thank you so much...

salim-barzani 1560
December 28 2024
0 0

@acer  last night my work stoped becuase of this physic i will not used anymore untill i something strange appear.

nothing,...

salim-barzani 1560
December 27 2024
0 0

@acer  just some time  a new sign appear with physic they remove , why problem is physic?

i like your code style...

salim-barzani 1560
December 27 2024
0 0

@mmcdara is different no one can undrestand except you  best of best thank you so much.

Thanks you, you did a great job...

salim-barzani 1560
December 27 2024
0 0

@mmcdara you are legend of the coding

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