The European Physical Journal Special Topics

, Volume 223, Issue 11, pp 2145–2159 | Cite as

Exploding dissipative solitons in the cubic-quintic complex Ginzburg-Landau equation in one and two spatial dimensions

A review and a perspective
Review
Part of the following topical collections:
  1. Dynamic Systems: From Statistical Mechanics to Engineering Applications

Abstract

We review the work on exploding dissipative solitons in one and two spatial dimensions. Features covered include: the transition from modulated to exploding dissipative solitons, the analogue of the Ruelle-Takens scenario for dissipative solitons, inducing exploding dissipative solitons by noise, two classes of exploding dissipative solitons in two spatial dimensions, diffusing asymmetric exploding dissipative solitons as a model for a two-dimensional extended chaotic system. As a perspective we outline the interaction of exploding dissipative solitons with quasi one-dimensional dissipative solitons, breathing quasi one-dimensional solutions and their possible connection with experimental results on convection, and the occurence of exploding dissipative solitons in reaction-diffusion systems.

It is a great pleasure to dedicate this work to our long-time friend Hans (Prof. Dr. Hans Jürgen Herrmann) on the occasion of his 60th birthday.

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Copyright information

© EDP Sciences and Springer 2014

Authors and Affiliations

  1. 1.Complex Systems Group, Facultad de Ingeniería y Ciencias Aplicadas, Universidad de los AndesSantiagoChile
  2. 2.Department of PhysicsUniversity of BayreuthBayreuthGermany

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