Polynomial Complex Ginzburg-Landau equations in almost periodic spaces

TL;DR

This paper investigates the well-posedness of polynomial complex Ginzburg-Landau equations in almost periodic spaces, demonstrating phase preservation under certain initial conditions using splitting methods.

Contribution

It introduces a novel approach to establish well-posedness in almost periodic spaces and shows phase preservation for solutions with irrational phase multiples.

Findings

Well-posedness established for polynomial complex Ginzburg-Landau equations in almost periodic spaces.

Solutions preserve initial irrational phase multiples over time.

Splitting methods effectively prove phase invariance and well-posedness.

Abstract

We consider Complex Ginzburg-Landau equations with a polynomial nonlinearity 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.