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Question: How isolate linear and non linear which contain conjugate part in equation?

Question:How isolate linear and non linear which contain conjugate part in equation?

salim-barzani 1550 Maple 2024
linear syntax selectremove conjugate
June 04 2025
0

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)
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with(PDEtools)
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with(DEtools)
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with(DifferentialAlgebra)
> 

"with(Student[ODEs][Solve]): "
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with(IntegrationTools)
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with(inttrans)
> 

with(PDEtools)
> 

with(Physics)
> 

with(PolynomialTools)
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with(RootFinding)
> 

with(SolveTools)
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with(LinearAlgebra)
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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

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