The exact solutions to the complex Ginzburg-Landau equation should not be searched for by perturbing some linear equation. Indeed, there exist methods to deal in one go with the full nonlinear equation. These are easier to implement than the perturbative methods and they rely only on the deepest feature of the equation, namely the structure of its singularities.
No takes yet. Share an insight, caveat, or question.
Conte et al. (1995) studied this question.
Synapse has enriched 5 related papers. Consider them for comparative context: