Damped wave dynamics for a complex Ginzburg-Landau equation with low dissipation

TL;DR

This paper analyzes a complex Ginzburg-Landau equation with low dissipation, showing that long-wave perturbations follow a damped wave dynamic and never vanish, providing insights into the equation's long-term behavior.

Contribution

It introduces a new asymptotic regime for low-dissipation Ginzburg-Landau equations and derives a damped wave model for long-wave perturbations.

Findings

Long-wave perturbations do not vanish.

Perturbations follow a damped wave dynamic.

The study provides a new asymptotic description for low dissipation.

Abstract

We consider a complex Ginzburg-Landau equation, corresponding to a Gross-Pitaevskii equation with a small dissipation term. We study an asymptotic regime for long-wave perturbations of constant maps of modulus one. We show that such solutions never vanish and we derive a damped wave dynamics for the perturbation.