Exploding dissipative solitons in the cubic-quintic complex Ginzburg-Landau equation in one and two spatial dimensions: A review and a perspective

C. Cartes, O. Descalzi*, H. R. Brand

*Corresponding author for this work

Research output: Contribution to journalReview articlepeer-review

6 Scopus citations

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.

Original languageEnglish
Pages (from-to)2145-2159
Number of pages15
JournalEuropean Physical Journal: Special Topics
Volume223
Issue number11
DOIs
StatePublished - 1 Oct 2014

Bibliographical note

Publisher Copyright:
© 2014, EDP Sciences and Springer.

Fingerprint

Dive into the research topics of 'Exploding dissipative solitons in the cubic-quintic complex Ginzburg-Landau equation in one and two spatial dimensions: A review and a perspective'. Together they form a unique fingerprint.

Cite this