Symmetry breaking term effects on explosive localized solitons
Complex Systems Group, Facultad de Ingeniería y Ciencias Aplicadas, Universidad de los Andes, Av. Mons. Alvaro del Portillo 12.455, Las Condes, Santiago, Chile
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Received: 11 September 2013
Revised: 25 November 2013
Published online: 23 January 2014
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.
© EDP Sciences, Springer-Verlag, 2014