Symmetry breaking term effects on explosive localized solitons

C. Cartes; O. Descalzi

doi:10.1140/epjst/e2014-02086-1

Symmetry breaking term effects on explosive localized solitons

C. Cartes^*, O. Descalzi

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

15 Scopus citations

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 s_c. 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 60^th birthday.

Original language	English
Pages (from-to)	91-98
Number of pages	8
Journal	European Physical Journal: Special Topics
Volume	223
Issue number	1
DOIs	https://doi.org/10.1140/epjst/e2014-02086-1
State	Published - Jan 2014

Bibliographical note

Funding Information:
The authors thanks to Jaime Anguita and Mário Ferreira for their useful comments. O.D. and C.C wish to thank the support of FONDECYT (Projects 11121228 and 1110360) and Universidad de los Andes through FAI initiatives.

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title = "Symmetry breaking term effects on explosive localized solitons",

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.",

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N1 - Funding Information: The authors thanks to Jaime Anguita and Mário Ferreira for their useful comments. O.D. and C.C wish to thank the support of FONDECYT (Projects 11121228 and 1110360) and Universidad de los Andes through FAI initiatives.

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N2 - 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.

AB - 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.

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Symmetry breaking term effects on explosive localized solitons

Abstract

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