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salim-barzani

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1 years, 12 days
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These are questions asked by salim-barzani

What is Idea behind finding parameter?...

salim-barzani 1555 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 1555 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 1555 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

Download p1.mw

How do convert language to Matlab when ...

salim-barzani 1555 Maple 2024
codegeneration matlab
February 13 2025
0 0

i don't know how apply conversation language to matlab in righ hand side  don't show up to do conversation language for short is come up but for this not 

> 

restart
> 

K := (2*(k[1]*exp((3/4)*k[1]*t*alpha*p[1]^2+(1/4)*t*k[1]^3+k[1]*p[1]*y+k[1]*x+k[1]*z+eta[1])+((p[1]-p[2])^2*alpha-(k[1]-k[2])^2)*(k[1]+k[2])*exp((3/4)*k[1]*t*alpha*p[1]^2+(1/4)*t*k[1]^3+k[1]*p[1]*y+k[1]*x+k[1]*z+eta[1]+(3/4)*k[2]*t*alpha*p[2]^2+(1/4)*t*k[2]^3+k[2]*p[2]*y+k[2]*x+k[2]*z+eta[2])/((p[1]-p[2])^2*alpha-(k[1]+k[2])^2)+k[2]*exp((3/4)*k[2]*t*alpha*p[2]^2+(1/4)*t*k[2]^3+k[2]*p[2]*y+k[2]*x+k[2]*z+eta[2])+((p[2]-p[3])^2*alpha-(k[2]-k[3])^2)*(k[2]+k[3])*exp((3/4)*k[2]*t*alpha*p[2]^2+(1/4)*t*k[2]^3+k[2]*p[2]*y+k[2]*x+k[2]*z+eta[2]+(3/4)*k[3]*t*alpha*p[3]^2+(1/4)*t*k[3]^3+k[3]*p[3]*y+k[3]*x+k[3]*z+eta[3])/((p[2]-p[3])^2*alpha-(k[2]+k[3])^2)+((p[1]-p[2])^2*alpha-(k[1]-k[2])^2)*((p[1]-p[3])^2*alpha-(k[1]-k[3])^2)*((p[2]-p[3])^2*alpha-(k[2]-k[3])^2)*(k[1]+k[2]+k[3])*exp((3/4)*k[1]*t*alpha*p[1]^2+(1/4)*t*k[1]^3+k[1]*p[1]*y+k[1]*x+k[1]*z+eta[1]+(3/4)*k[2]*t*alpha*p[2]^2+(1/4)*t*k[2]^3+k[2]*p[2]*y+k[2]*x+k[2]*z+eta[2]+(3/4)*k[3]*t*alpha*p[3]^2+(1/4)*t*k[3]^3+k[3]*p[3]*y+k[3]*x+k[3]*z+eta[3])/(((p[1]-p[2])^2*alpha-(k[1]+k[2])^2)*((p[1]-p[3])^2*alpha-(k[1]+k[3])^2)*((p[2]-p[3])^2*alpha-(k[2]+k[3])^2))+((p[1]-p[3])^2*alpha-(k[1]-k[3])^2)*(k[1]+k[3])*exp((3/4)*k[1]*t*alpha*p[1]^2+(1/4)*t*k[1]^3+k[1]*p[1]*y+k[1]*x+k[1]*z+eta[1]+(3/4)*k[3]*t*alpha*p[3]^2+(1/4)*t*k[3]^3+k[3]*p[3]*y+k[3]*x+k[3]*z+eta[3])/((p[1]-p[3])^2*alpha-(k[1]+k[3])^2)+k[3]*exp((3/4)*k[3]*t*alpha*p[3]^2+(1/4)*t*k[3]^3+k[3]*p[3]*y+k[3]*x+k[3]*z+eta[3])))/(1+exp((3/4)*k[1]*t*alpha*p[1]^2+(1/4)*t*k[1]^3+k[1]*p[1]*y+k[1]*x+k[1]*z+eta[1])+((p[1]-p[2])^2*alpha-(k[1]-k[2])^2)*exp((3/4)*k[1]*t*alpha*p[1]^2+(1/4)*t*k[1]^3+k[1]*p[1]*y+k[1]*x+k[1]*z+eta[1]+(3/4)*k[2]*t*alpha*p[2]^2+(1/4)*t*k[2]^3+k[2]*p[2]*y+k[2]*x+k[2]*z+eta[2])/((p[1]-p[2])^2*alpha-(k[1]+k[2])^2)+exp((3/4)*k[2]*t*alpha*p[2]^2+(1/4)*t*k[2]^3+k[2]*p[2]*y+k[2]*x+k[2]*z+eta[2])+((p[2]-p[3])^2*alpha-(k[2]-k[3])^2)*exp((3/4)*k[2]*t*alpha*p[2]^2+(1/4)*t*k[2]^3+k[2]*p[2]*y+k[2]*x+k[2]*z+eta[2]+(3/4)*k[3]*t*alpha*p[3]^2+(1/4)*t*k[3]^3+k[3]*p[3]*y+k[3]*x+k[3]*z+eta[3])/((p[2]-p[3])^2*alpha-(k[2]+k[3])^2)+((p[1]-p[2])^2*alpha-(k[1]-k[2])^2)*((p[1]-p[3])^2*alpha-(k[1]-k[3])^2)*((p[2]-p[3])^2*alpha-(k[2]-k[3])^2)*exp((3/4)*k[1]*t*alpha*p[1]^2+(1/4)*t*k[1]^3+k[1]*p[1]*y+k[1]*x+k[1]*z+eta[1]+(3/4)*k[2]*t*alpha*p[2]^2+(1/4)*t*k[2]^3+k[2]*p[2]*y+k[2]*x+k[2]*z+eta[2]+(3/4)*k[3]*t*alpha*p[3]^2+(1/4)*t*k[3]^3+k[3]*p[3]*y+k[3]*x+k[3]*z+eta[3])/(((p[1]-p[2])^2*alpha-(k[1]+k[2])^2)*((p[1]-p[3])^2*alpha-(k[1]+k[3])^2)*((p[2]-p[3])^2*alpha-(k[2]+k[3])^2))+((p[1]-p[3])^2*alpha-(k[1]-k[3])^2)*exp((3/4)*k[1]*t*alpha*p[1]^2+(1/4)*t*k[1]^3+k[1]*p[1]*y+k[1]*x+k[1]*z+eta[1]+(3/4)*k[3]*t*alpha*p[3]^2+(1/4)*t*k[3]^3+k[3]*p[3]*y+k[3]*x+k[3]*z+eta[3])/((p[1]-p[3])^2*alpha-(k[1]+k[3])^2)+exp((3/4)*k[3]*t*alpha*p[3]^2+(1/4)*t*k[3]^3+k[3]*p[3]*y+k[3]*x+k[3]*z+eta[3]))

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

 (1)
 

NULL

Download convert-to-matlab.mw

Why my eval command not apply ? and How ...

salim-barzani 1555 Maple
parameters eval substitution
February 09 2025
1 1

i want to get zero of this function i did all part true but i don't know why my pde not getting zero after substitute each parameter and part 

> 

restart
> 

with(PDEtools)
> 

NULL
> 

undeclare(prime)

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

 (1)
> 

p := 2*k; n := 1; xi := -p*t+x

2*k

  

1

  

-2*k*t+x

 (2)
> 

"U(xi):=(B[1] (RootOf(3 _Z^2-3 _Z-1)+coth(xi)))^(-1/n);u(x,t):=(B[1] (RootOf(3 _Z^2-3 _Z-1)+coth(-p t+x)))^(-1/n) (e)^(ⅈ (k x-t w))"

proc (xi) options operator, arrow, function_assign; (B[1]*(RootOf(3*_Z^2-3*_Z-1)+coth(xi)))^(-1/n) end proc

  

proc (x, t) options operator, arrow, function_assign; (B[1]*(RootOf(3*_Z^2-3*_Z-1)+coth(-p*t+x)))^(-1/n)*exp(I*(k*x-t*w)) end proc

 (3)
> 

pde := I*(diff(u(x, t), t))+diff(u(x, t), `$`(x, 2))+eta*u(x, t)+beta*U(xi)^n*u(x, t)+gamma*U(xi)^(2*n)*u(x, t)+delta*U(xi)^(3*n)*u(x, t)+lambda*U(xi)^(4*n)*u(x, t) = 0

I*(2*exp(I*(k*x-t*w))*k*(1-coth(2*k*t-x)^2)/(B[1]*(RootOf(3*_Z^2-3*_Z-1)-coth(2*k*t-x))^2)-I*w*exp(I*(k*x-t*w))/(B[1]*(RootOf(3*_Z^2-3*_Z-1)-coth(2*k*t-x))))+2*exp(I*(k*x-t*w))*(1-coth(2*k*t-x)^2)^2/(B[1]*(RootOf(3*_Z^2-3*_Z-1)-coth(2*k*t-x))^3)-(2*I)*k*exp(I*(k*x-t*w))*(1-coth(2*k*t-x)^2)/(B[1]*(RootOf(3*_Z^2-3*_Z-1)-coth(2*k*t-x))^2)+2*exp(I*(k*x-t*w))*coth(2*k*t-x)*(-1+coth(2*k*t-x)^2)/(B[1]*(RootOf(3*_Z^2-3*_Z-1)-coth(2*k*t-x))^2)-k^2*exp(I*(k*x-t*w))/(B[1]*(RootOf(3*_Z^2-3*_Z-1)-coth(2*k*t-x)))+eta*exp(I*(k*x-t*w))/(B[1]*(RootOf(3*_Z^2-3*_Z-1)-coth(2*k*t-x)))+beta*exp(I*(k*x-t*w))/(B[1]^2*(RootOf(3*_Z^2-3*_Z-1)-coth(2*k*t-x))^2)+gamma*exp(I*(k*x-t*w))/(B[1]^3*(RootOf(3*_Z^2-3*_Z-1)-coth(2*k*t-x))^3)+delta*exp(I*(k*x-t*w))/(B[1]^4*(RootOf(3*_Z^2-3*_Z-1)-coth(2*k*t-x))^4)+lambda*exp(I*(k*x-t*w))/(B[1]^5*(RootOf(3*_Z^2-3*_Z-1)-coth(2*k*t-x))^5) = 0

 (4)
> 

case1 := [beta = 2*RootOf(3*_Z^2-3*_Z-1)*(n+2)/(B[1]*n^2), delta = 2*B[1]*(RootOf(3*_Z^2-3*_Z-1)+1)*(3*n+2)/(3*n^2), eta = (k^2*n^2*B[1]^2-n^2*w*B[1]^2-1)/(n^2*B[1]^2), gamma = -6*RootOf(3*_Z^2-3*_Z-1)*(n+1)/n^2, lambda = B[1]^2*(3*RootOf(3*_Z^2-3*_Z-1)-7)*(2*n+1)/(9*n^2), A[0] = RootOf(3*_Z^2-3*_Z-1)*B[1], A[1] = 0, B[1] = B[1]]

[beta = 6*RootOf(3*_Z^2-3*_Z-1)/B[1], delta = (10/3)*B[1]*(RootOf(3*_Z^2-3*_Z-1)+1), eta = (k^2*B[1]^2-w*B[1]^2-1)/B[1]^2, gamma = -12*RootOf(3*_Z^2-3*_Z-1), lambda = (1/3)*B[1]^2*(3*RootOf(3*_Z^2-3*_Z-1)-7), A[0] = RootOf(3*_Z^2-3*_Z-1)*B[1], A[1] = 0, B[1] = B[1]]

 (5)
> 

pde3 := eval(pde, case1)
 

``

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