Dynamics of spiral waves in the complex Ginzburg-Landau equation in bounded domains

TL;DR

This paper analyzes how boundaries influence spiral wave dynamics in the complex Ginzburg-Landau equation, deriving explicit motion laws and showing exponential slowing of spirals beyond a critical twist parameter.

Contribution

It provides explicit laws of spiral motion in bounded domains and reveals the exponential slowdown of spirals when the twist parameter surpasses a critical value.

Findings

Spiral motion laws are explicitly derived for rectangular domains.

Spiral speed becomes exponentially slow beyond a critical twist parameter.

Oscillation frequency of multiple-spiral patterns is analytically obtained.

Abstract

Multiple-spiral-wave solutions of the general cubic complex Ginzburg-Landau equation in bounded domains are considered. We investigate the effect of the boundaries on spiral motion under homogeneous Neumann boundary conditions, for small values of the twist parameter $q$. We derive explicit laws of motion for rectangular domains and we show that the motion of spirals becomes exponentially slow when the twist parameter exceeds a critical value depending on the size of the domain. The oscillation frequency of multiple-spiral patterns is also analytically obtained.