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?
