Thanks for your interest @dharr,

We also know that q(x,t) is a complex function. There is no other assumption.

I don't understand the following step in your code. Could you explain it more?

subs(abs(q(x,t))=psi(xi) ,PDE):

On the other hand, I checked your code for different PDE as follows: 

where u(x,t) is a complex function.

Using the following transformation:

one can derive that (I got the PDE above and the following result from another paper)

I edited your code a little bit and I think that I got the same results in the paper.

If you want, you can check the newcode.mw

Thanks again.