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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 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 60th birthday.

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Authors and Affiliations

  1. Complex Systems Group, Facultad de Ingeniería y Ciencias Aplicadas, Universidad de los Andes, Av. Mons. Alvaro del Portillo, 12.455, Las Condes, Santiago, Chile

    C. Cartes & O. Descalzi

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  1. C. Cartes
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  2. O. Descalzi
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Correspondence to C. Cartes.

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Cartes, C., Descalzi, O. Symmetry breaking term effects on explosive localized solitons. Eur. Phys. J. Spec. Top. 223, 91–98 (2014). https://doi.org/10.1140/epjst/e2014-02086-1

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  • DOI: https://doi.org/10.1140/epjst/e2014-02086-1

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