in this substitution really is hard to substitute which i don't have idea how find u[1]  u[2] so on becuase  in that term some function like u[i,x] appear and i don't have idea how define them to remove it in my iteration ? and how remove the conjugate of function u[0] i did try evalc(u[0]) and make it worst than this 

which i did some special substitution which i don't know true or not but result is true i didn't have other idea for that
which  instead of any conjugate i use v and istead of any diff(u,x) i use z[i,x] and if conjugate have derivative v[i,x]

k4.mw

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?

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