Phase Diagram of the Two-Dimensional Complex Ginzburg-Landau Equation

TL;DR

This paper reviews the complex Ginzburg-Landau equation in two dimensions, presenting a comprehensive numerical phase diagram, analyzing phase transitions, and discussing related theoretical challenges.

Contribution

It provides the first extensive numerical phase diagram of the 2D complex Ginzburg-Landau equation and explores the nature of phase transitions and theoretical issues.

Findings

Identification of distinct phases in the parameter space

Characterization of phase transition types

Discussion of theoretical problems related to the phase diagram

Abstract

After a brief introduction to the complex Ginzburg-Landau equation, some of its important features in two space dimensions are reviewed. A comprehensive study of the various phases observed numerically in large systems over the whole parameter space is then presented. The nature of the transitions between these phases is investigated and some theoretical problems linked to the phase diagram are discussed.