Polynomial Complex Ginzburg-Landau equations in almost periodic spaces

Abstract
We consider complex Ginzburg-Landau equations with a polynomial non-linearity in the real line. We use splitting-methods to prove well-posedness for a subset of almost periodic spaces. Specifically, we prove that if the initial condition has multiples of an irrational phase, then the solution of the equation maintains those same phases.
Description
Keywords
mathematics, analysis of PDEs, 47J35, 35K55, 35K58
Citation
Besteiro, A. (2023). Polynomial Complex Ginzburg-Landau equations in almost periodic spaces. In: Communications in Mathematics 31(1):91-101