I have a nonlinear Schrodinger equation which reads:

$$ \frac{1}{2} \frac{d^2u}{dx^2}+ |u|^2u + V(x)u = -i \frac{du}{dz},$$

where $V(x)=\cos(wx)+ i a \sin(wx)$ and $w$, $a$ are numbers.

How to solve its band structure, meaning its dispersion relation?

The plane wave expansion method is used for a real potential. Can it be applied for this complex potential also?

What are other methods, if any, in Matlab or Mathematica or other software?

  • $\begingroup$ welcome to scicomp! please use mathjax to format your equations. $\endgroup$
    – GoHokies
    Dec 21 '17 at 10:48
  • $\begingroup$ I think that you should not have a source term to compute the dispersion relation $\endgroup$
    – nicoguaro
    Dec 21 '17 at 13:59
  • $\begingroup$ @ Kirill : Yes you're right, it was just a typo. $\endgroup$
    – foi
    Dec 22 '17 at 11:42

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