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.
Soliton Explosive Graphical Processing Unit European Physical Journal Special Topic Propagation Distance
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