Symmetry breaking term effects on explosive localized solitons

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Abstract

We study the influence of an analog of self-steepening (SST), which is a term breaking the T →-T symmetry, on explosive localized solutions for the cubic-quintic complex Ginzburg-Landau equation in the anomalous dispersion regime. We find that while this explosive behavior occurs for a wide range of the parameter s, characterizing SST, the mean distance between explosions diverges close to a critical value sc. After this value the explosive solution becomes a fixed shape soliton that moves at constant speed. The transition between explosive and regular behavior is characterized by a transcritical bifurcation controlled by the SST parameter. We also proposed a mechanism which explains and predicts the mean distance between explosions as a function of s. We are glad to dedicate this article to Professor Helmut R. Brand on occasion of his 60th birthday.
Original languageAmerican English
Pages (from-to)91-98
Number of pages8
JournalEuropean Physical Journal: Special Topics
Volume223
Issue number1
DOIs
StatePublished - 1 Jan 2014

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