Complex Ginzburg-Landau equation

Question

Hi there, I was wondering if there is a way to integrate 2D and 3D versions of the Complex Ginzburg-Landau equation? The flow equations simply reads:

$${\psi _t} = \psi + \left( {1 + i\alpha } \right){\nabla ^2}\psi - \left( {1 + i\beta } \right){\left| \psi \right|^2}\psi $$

Answer 1

FEniCS doesn't support complex-valued functions yet, so you'll have to take the detour of splitting the equation up into real and imaginary part. (It might help to express $|\psi|^2$ as $\psi*\psi$ here.)

From here on it's just a matter of implementing a simple time-stepping scheme; check out the documentation for time-depentend problems.

Whether the domain is 2D or 3D doesn't matter for the weak form; everything is supported.