Ordered and self-disordered dynamics of holes and defects in the one-dimensional complex Ginzburg-Landau equation

Abstract

We study the dynamics of holes and defects in the 1D complex Ginzburg--Landau equation in ordered and chaotic cases. Ordered hole--defect dynamics occurs when an unstable hole invades a plane wave state and periodically nucleates defects from which new holes are born. The results of a detailed numerical study of these periodic states are incorporated into a simple analytic description of isolated "edge" holes. Extending this description, we obtain a minimal model for general hole--defect dynamics. We show that interactions between the holes and a self--disordered background are essential for the occurrence of spatiotemporal chaos in hole--defect states.

Extensive revision; accepted for PRL

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• The dynamics of vortex lines in the three-dimensional complex Ginzburg-Landau equation: instability, stretching, entanglement, and helices
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