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salim-barzani

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1 years, 327 days
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These are questions asked by salim-barzani

How by apply limit remove the constant...

salim-barzani 1765 Maple 2024
limit duplicate-question
February 16 2025
0 5

How apply long wave limit for removing the constant k in such function , i need a general formula 

Limiting process from eq 12 to Bij

> 

restart
> 

NULL

Eq 12.

> 

eij := ((-3*k[i]*(k[i]-k[j])*l[j]+beta)*l[i]^2-(2*(-3*k[j]*(k[i]-k[j])*l[j]*(1/2)+beta))*l[j]*l[i]+beta*l[j]^2)/((-3*k[i]*(k[i]+k[j])*l[j]+beta)*l[i]^2-(2*(3*k[j]*(k[i]+k[j])*l[j]*(1/2)+beta))*l[j]*l[i]+beta*l[j]^2)

((-3*k[i]*(k[i]-k[j])*l[j]+beta)*l[i]^2-2*(-(3/2)*k[j]*(k[i]-k[j])*l[j]+beta)*l[j]*l[i]+beta*l[j]^2)/((-3*k[i]*(k[i]+k[j])*l[j]+beta)*l[i]^2-2*((3/2)*k[j]*(k[i]+k[j])*l[j]+beta)*l[j]*l[i]+beta*l[j]^2)

 (1)
> 

eval(eij, k[j] = k[i]); series(%, k[i], 3); convert(%, polynom); eval(%, k[j] = k[i]); Bij := %

(beta*l[i]^2-2*beta*l[i]*l[j]+beta*l[j]^2)/((-6*k[i]^2*l[j]+beta)*l[i]^2-2*(3*k[i]^2*l[j]+beta)*l[j]*l[i]+beta*l[j]^2)

  

series(1+((6*l[i]^2*l[j]+6*l[i]*l[j]^2)/(beta*l[i]^2-2*beta*l[i]*l[j]+beta*l[j]^2))*k[i]^2+O(k[i]^4),k[i],4)

  

1+(6*l[i]^2*l[j]+6*l[i]*l[j]^2)*k[i]^2/(beta*l[i]^2-2*beta*l[i]*l[j]+beta*l[j]^2)

  

1+(6*l[i]^2*l[j]+6*l[i]*l[j]^2)*k[i]^2/(beta*l[i]^2-2*beta*l[i]*l[j]+beta*l[j]^2)

  

1+(6*l[i]^2*l[j]+6*l[i]*l[j]^2)*k[i]^2/(beta*l[i]^2-2*beta*l[i]*l[j]+beta*l[j]^2)

 (2)
> 

NULL

NULL

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How collect a fraction which contain der...

salim-barzani 1765 Maple 2024
parameters pde differential-equations
February 15 2025
1 9

i want construct a series trail function for all pdf not just this one but this is a easy one, also after replacing the function How i can collect variable and make algebraic system for finding the constant of series function like a[20],a[10],a[00]. where i is number of derivative by x and n is number of derivative by t also n=0 and m=2 

> 

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))

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

 (2)
> 

declare(w(x, t))

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

 (3)
> 

pde := diff(u(x, t), t)+u(x, t)*(diff(u(x, t), x))+delta*(diff(u(x, t), `$`(x, 3))) = 0

diff(u(x, t), t)+u(x, t)*(diff(u(x, t), x))+delta*(diff(diff(diff(u(x, t), x), x), x)) = 0

 (4)
> 

NULL
> 

K := u(x, t) = a[20]*(diff(ln(w(x, t)), `$`(x, 2)))+a[10]*(diff(ln(w(x, t)), x))+a[0]

u(x, t) = a[20]*((diff(diff(w(x, t), x), x))/w(x, t)-(diff(w(x, t), x))^2/w(x, t)^2)+a[10]*(diff(w(x, t), x))/w(x, t)+a[0]

 (5)
> 

K1 := normal(eval(pde, K))

(w(x, t)^4*(diff(diff(w(x, t), x), x))*a[0]*a[10]+w(x, t)^4*(diff(diff(diff(w(x, t), x), x), x))*a[0]*a[20]+w(x, t)^4*(diff(diff(diff(diff(diff(w(x, t), x), x), x), x), x))*delta*a[20]+w(x, t)^4*(diff(diff(diff(diff(w(x, t), x), x), x), x))*delta*a[10]-3*w(x, t)^3*(diff(diff(w(x, t), x), x))^2*delta*a[10]+w(x, t)^3*(diff(diff(w(x, t), x), x))^2*a[10]*a[20]+w(x, t)^3*(diff(diff(w(x, t), x), x))*(diff(w(x, t), x))*a[10]^2+w(x, t)^3*(diff(diff(w(x, t), x), x))*(diff(diff(diff(w(x, t), x), x), x))*a[20]^2-w(x, t)^3*(diff(w(x, t), x))^2*a[0]*a[10]-3*w(x, t)^2*(diff(diff(w(x, t), x), x))^2*(diff(w(x, t), x))*a[20]^2+2*w(x, t)^2*(diff(w(x, t), x))^3*a[0]*a[20]-w(x, t)^2*(diff(w(x, t), x))^2*(diff(diff(diff(w(x, t), x), x), x))*a[20]^2+5*w(x, t)*(diff(diff(w(x, t), x), x))*(diff(w(x, t), x))^3*a[20]^2-6*w(x, t)*(diff(w(x, t), x))^4*delta*a[10]+3*w(x, t)*(diff(w(x, t), x))^4*a[10]*a[20]-w(x, t)^3*(diff(diff(w(x, t), x), x))*(diff(w(x, t), t))*a[20]-a[10]*(diff(w(x, t), x))*(diff(w(x, t), t))*w(x, t)^3-2*w(x, t)^3*(diff(w(x, t), x))*(diff(diff(w(x, t), t), x))*a[20]+2*w(x, t)^2*(diff(w(x, t), t))*(diff(w(x, t), x))^2*a[20]-3*w(x, t)^3*(diff(diff(w(x, t), x), x))*(diff(w(x, t), x))*a[0]*a[20]-10*w(x, t)^3*(diff(diff(w(x, t), x), x))*(diff(diff(diff(w(x, t), x), x), x))*delta*a[20]-4*w(x, t)^3*(diff(w(x, t), x))*(diff(diff(diff(w(x, t), x), x), x))*delta*a[10]+w(x, t)^3*(diff(w(x, t), x))*(diff(diff(diff(w(x, t), x), x), x))*a[10]*a[20]-5*w(x, t)^3*(diff(w(x, t), x))*(diff(diff(diff(diff(w(x, t), x), x), x), x))*delta*a[20]+30*w(x, t)^2*(diff(diff(w(x, t), x), x))^2*(diff(w(x, t), x))*delta*a[20]+12*w(x, t)^2*(diff(diff(w(x, t), x), x))*(diff(w(x, t), x))^2*delta*a[10]-5*w(x, t)^2*(diff(diff(w(x, t), x), x))*(diff(w(x, t), x))^2*a[10]*a[20]+20*w(x, t)^2*(diff(w(x, t), x))^2*(diff(diff(diff(w(x, t), x), x), x))*delta*a[20]-60*w(x, t)*(diff(diff(w(x, t), x), x))*(diff(w(x, t), x))^3*delta*a[20]-w(x, t)^2*(diff(w(x, t), x))^3*a[10]^2+24*(diff(w(x, t), x))^5*delta*a[20]+(diff(diff(diff(w(x, t), t), x), x))*w(x, t)^4*a[20]+a[10]*(diff(diff(w(x, t), t), x))*w(x, t)^4-2*(diff(w(x, t), x))^5*a[20]^2)/w(x, t)^5 = 0

 (6)
> 

K2 := expand(%)

(diff(diff(w(x, t), x), x))*a[0]*a[10]/w(x, t)+(diff(diff(diff(w(x, t), x), x), x))*a[0]*a[20]/w(x, t)+(diff(diff(diff(diff(diff(w(x, t), x), x), x), x), x))*delta*a[20]/w(x, t)+(diff(diff(diff(diff(w(x, t), x), x), x), x))*delta*a[10]/w(x, t)-3*(diff(diff(w(x, t), x), x))^2*delta*a[10]/w(x, t)^2+(diff(diff(w(x, t), x), x))^2*a[10]*a[20]/w(x, t)^2+(diff(diff(w(x, t), x), x))*(diff(w(x, t), x))*a[10]^2/w(x, t)^2+(diff(diff(w(x, t), x), x))*(diff(diff(diff(w(x, t), x), x), x))*a[20]^2/w(x, t)^2-(diff(w(x, t), x))^2*a[0]*a[10]/w(x, t)^2-3*(diff(diff(w(x, t), x), x))^2*(diff(w(x, t), x))*a[20]^2/w(x, t)^3+2*(diff(w(x, t), x))^3*a[0]*a[20]/w(x, t)^3-(diff(w(x, t), x))^2*(diff(diff(diff(w(x, t), x), x), x))*a[20]^2/w(x, t)^3+5*(diff(diff(w(x, t), x), x))*(diff(w(x, t), x))^3*a[20]^2/w(x, t)^4-6*(diff(w(x, t), x))^4*delta*a[10]/w(x, t)^4+3*(diff(w(x, t), x))^4*a[10]*a[20]/w(x, t)^4-(diff(diff(w(x, t), x), x))*(diff(w(x, t), t))*a[20]/w(x, t)^2-a[10]*(diff(w(x, t), x))*(diff(w(x, t), t))/w(x, t)^2-2*(diff(w(x, t), x))*(diff(diff(w(x, t), t), x))*a[20]/w(x, t)^2+2*(diff(w(x, t), t))*(diff(w(x, t), x))^2*a[20]/w(x, t)^3+24*(diff(w(x, t), x))^5*delta*a[20]/w(x, t)^5+20*(diff(w(x, t), x))^2*(diff(diff(diff(w(x, t), x), x), x))*delta*a[20]/w(x, t)^3-60*(diff(diff(w(x, t), x), x))*(diff(w(x, t), x))^3*delta*a[20]/w(x, t)^4-3*(diff(diff(w(x, t), x), x))*(diff(w(x, t), x))*a[0]*a[20]/w(x, t)^2-10*(diff(diff(w(x, t), x), x))*(diff(diff(diff(w(x, t), x), x), x))*delta*a[20]/w(x, t)^2-4*(diff(w(x, t), x))*(diff(diff(diff(w(x, t), x), x), x))*delta*a[10]/w(x, t)^2+(diff(w(x, t), x))*(diff(diff(diff(w(x, t), x), x), x))*a[10]*a[20]/w(x, t)^2-5*(diff(w(x, t), x))*(diff(diff(diff(diff(w(x, t), x), x), x), x))*delta*a[20]/w(x, t)^2+30*(diff(diff(w(x, t), x), x))^2*(diff(w(x, t), x))*delta*a[20]/w(x, t)^3+12*(diff(diff(w(x, t), x), x))*(diff(w(x, t), x))^2*delta*a[10]/w(x, t)^3-5*(diff(diff(w(x, t), x), x))*(diff(w(x, t), x))^2*a[10]*a[20]/w(x, t)^3-(diff(w(x, t), x))^3*a[10]^2/w(x, t)^3+(diff(diff(diff(w(x, t), t), x), x))*a[20]/w(x, t)+a[10]*(diff(diff(w(x, t), t), x))/w(x, t)-2*(diff(w(x, t), x))^5*a[20]^2/w(x, t)^5 = 0

 (7)

NULL

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What is Idea behind finding parameter?...

salim-barzani 1765 Maple 2024
parameters exponential pde
February 15 2025
0 10

I need to find parameter a[12] any one have any vision for finding parameter  , in p2a must contain 3 exponential but we recieve 19 of them which is something i think it is trail function but trail is give me result so must be a way for finding parameter 

a[12]-pde.mw

How can check pdetest when function is n...

salim-barzani 1765 Maple 2024
explore pde differential-equations
February 14 2025
0 4

the function is true but i want to be sure when i use pdetest must give me zero, but there must be a way for checking such function, please if your pc not strong don't click the command pdetest, i want use explore for such function but i am not sure it work or not, becuase the graph are a little bit strange  and long , i want  a way for easy plotting and visualization of such graph , can anyone help for solve this issue?

 sol.mw

How apply conjugate for getting result o...

salim-barzani 1765 Maple 2024
pde differential-equations conjugate
February 13 2025
1 1

i did pdetest without conjugate like the paper did i get zero but when i did pde test  with conjugate i didn't where is my problem 
i will do without conjugate but how change p[2]=conjugate(p[1])

> 

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, y, z, t))

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

 (2)
> 

declare(f(x, y, z, t))

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

 (3)
> 

pde := -4*(diff(u(x, y, z, t), x, t))+diff(u(x, y, z, t), `$`(x, 3), z)+3*alpha*(diff(u(x, y, z, t), `$`(y, 2)))+4*(diff(u(x, y, z, t), x))*(diff(u(x, y, z, t), x, z))+2*(diff(u(x, y, z, t), `$`(x, 2)))*(diff(u(x, y, z, t), z))

-4*(diff(diff(u(x, y, z, t), t), x))+diff(diff(diff(diff(u(x, y, z, t), x), x), x), z)+3*alpha*(diff(diff(u(x, y, z, t), y), y))+4*(diff(u(x, y, z, t), x))*(diff(diff(u(x, y, z, t), x), z))+2*(diff(diff(u(x, y, z, t), x), x))*(diff(u(x, y, z, t), z))

 (4)
> 

pde_nonlinear, pde_linear := selectremove(proc (term) options operator, arrow; has((eval(term, u(x, y, z, t) = a*u(x, y, z, t)))/a, a) end proc, pde)

4*(diff(u(x, y, z, t), x))*(diff(diff(u(x, y, z, t), x), z))+2*(diff(diff(u(x, y, z, t), x), x))*(diff(u(x, y, z, t), z)), -4*(diff(diff(u(x, y, z, t), t), x))+diff(diff(diff(diff(u(x, y, z, t), x), x), x), z)+3*alpha*(diff(diff(u(x, y, z, t), y), y))

 (5)
> 

thetai := t*w[i]+y*p[i]+x+z

t*w[i]+y*p[i]+x+z

 (6)
> 

eqw := w[i] = 3*alpha*p[i]^2*(1/4)

w[i] = (3/4)*alpha*p[i]^2

 (7)
> 

Bij := proc (i, j) options operator, arrow; 4/((p[i]-p[j])^2*alpha) end proc

proc (i, j) options operator, arrow; 4/((p[i]-p[j])^2*alpha) end proc

 (8)
> 

theta1 := normal(eval(eval(thetai, eqw), i = 1)); theta2 := normal(eval(eval(thetai, eqw), i = 2))

(3/4)*alpha*t*p[1]^2+y*p[1]+x+z

  

(3/4)*alpha*t*p[2]^2+y*p[2]+x+z

 (9)
> 

eqf := f(x, y, z, t) = theta1*theta2+4/((p[1]-p[2])^2*alpha)

f(x, y, z, t) = ((3/4)*alpha*t*p[1]^2+y*p[1]+x+z)*((3/4)*alpha*t*p[2]^2+y*p[2]+x+z)+4/((p[1]-p[2])^2*alpha)

 (10)
> 

eq17 := u(x, y, z, t) = 2*(diff(ln(f(x, y, z, t)), x))

u(x, y, z, t) = 2*(diff(f(x, y, z, t), x))/f(x, y, z, t)

 (11)
> 

eqt := eval(eq17, eqf)

u(x, y, z, t) = 2*((3/4)*alpha*t*p[2]^2+y*p[2]+2*x+2*z+(3/4)*alpha*t*p[1]^2+y*p[1])/(((3/4)*alpha*t*p[1]^2+y*p[1]+x+z)*((3/4)*alpha*t*p[2]^2+y*p[2]+x+z)+4/((p[1]-p[2])^2*alpha))

 (12)
> 

NULL
> 

pdetest(eqt, pde)

0

 (13)
> 

NULL

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