salim-barzani

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These are questions asked by salim-barzani

is easy to determine the linear and non linear part but how we can do it by command specially when contain conjugate part of function even i try to use another function instead of conjugate but stil i didn't got  the result?

restart

with(inttrans)

with(PDEtools)

with(DEtools)

with(DifferentialAlgebra)

"with(Student[ODEs][Solve]): "

with(IntegrationTools)

with(inttrans)

with(PDEtools)

with(Physics)

with(PolynomialTools)

with(RootFinding)

with(SolveTools)

with(LinearAlgebra)

with(sumtools)

declare(u(x, t))*conjugate(u(x, t))*declare(v(x, t))

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

 

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

 

conjugate(u(x, t))

(1)

pde := u(x, t)+I*(diff(u(x, t), `$`(x, 2)))+2*(diff(u(x, t)*conjugate(u(x, t)), x))*u(x, t)+u(x, t)^2*conjugate(u(x, t))^2*u(x, t) = 0

u(x, t)+I*(diff(diff(u(x, t), x), x))+2*((diff(u(x, t), x))*conjugate(u(x, t))+u(x, t)*(diff(conjugate(u(x, t)), x)))*u(x, t)+u(x, t)^3*conjugate(u(x, t))^2 = 0

(2)

pde_linear, pde_nonlinear := selectremove(proc (term) options operator, arrow; not has((eval(term, u(x, t) = T*u(x, t)))/T, T) end proc, expand(pde))

() = 0, u(x, t)+I*(diff(diff(u(x, t), x), x))+2*u(x, t)*(diff(u(x, t), x))*conjugate(u(x, t))+2*u(x, t)^2*(diff(conjugate(u(x, t)), x))+u(x, t)^3*conjugate(u(x, t))^2 = ()

(3)

u_occurrences := map(proc (i) options operator, arrow; numelems(select(has, [op([op(i)])], u)) end proc, oppde); linear_op_indices := ListTools:-SearchAll(1, u_occurrences); pde_linear := add(oppde[[linear_op_indices]]); pde_nonlinear := expand(simplify(expand(pde)-pde_linear))

Error, invalid input: ListTools:-SearchAll expects its 2nd argument, L, to be of type {list, rtable}, but received 0

 

[linear_op_indices]

 

Error, (in simpl/relopsum) invalid terms in sum: u(x,t)+I*diff(diff(u(x,t),x),x)+2*u(x,t)*diff(u(x,t),x)*conjugate(u(x,t))+2*u(x,t)^2*diff(conjugate(u(x,t)),x)+u(x,t)^3*conjugate(u(x,t))^2 = 0

 
 

NULL

Download solving.mw


How i can fix this issue ?
 

Download pdetest.mw

I used Maple’s odetest to check the validity of 36 exact solutions.

About half of them return zero, meaning they satisfy the ODE correctly. But the other half don’t — odetest gives nonzero expressions.

My question is:

Could there be a mistake in my assumptions, or are some of these solutions only valid under specific conditions?

I’d appreciate any clarification or suggestions.

ode-test-36.mw

Hi everyone,

I've encountered something odd while working with Maple's pdetest function. When I manually evaluate my proposed solution using eval() followed by simplify(), I get the expected identity 0 = 0, which suggests the solution satisfies the PDE. However, when I test the same solution using pdetest, it doesn't return zero. This inconsistency has left me unsure whether my solution is actually valid or if I'm missing something.

Has anyone else experienced this kind of discrepancy? Could this be due to how pdetest handles derivatives or symbolic simplification internally?

Any insights or suggestions would be greatly appreciated!

Download pde-test.mw

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