Ginzburg-Landau Spiral Waves in Circular and Spherical Geometries

TL;DR

This paper proves the existence of various spiral wave solutions in the complex Ginzburg-Landau equation on circular and spherical geometries, introducing new bifurcation methods and identifying novel patterns.

Contribution

It introduces a new global bifurcation approach and extends the existence results to include frozen spirals and 2-tip spirals in these geometries.

Findings

Existence of m-armed spiral waves in circular and spherical geometries

Discovery of frozen spiral patterns in both geometries

Identification of 2-tip spiral patterns in spherical geometry

Abstract

We prove the existence of $m$-armed spiral wave solutions for the complex Ginzburg-Landau equation in the circular and spherical geometries. We establish a new global bifurcation approach and generalize the results of existence for rigidly-rotating spiral waves. Moreover, we prove the existence of two new patterns: frozen spirals in the circular and spherical geometries, and 2-tip spirals in the spherical geometry.