Non-unique results of collisions of quasi-one-dimensional dissipative solitons

Orazio Descalzi, Helmut R. Brand

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Abstract

We investigate collisions of quasi-one-dimensional dissipative solitons (DSs) for a large class of initial conditions, which are not temporally asymptotic quasi-one-dimensional DSs. For the case of sufficiently small approach velocity and sufficiently large values of the dissipative cross-coupling between the counterpropagating DSs, we find non-unique results for the outcome of collisions. We demonstrate that these non-unique results are intrinsically related to a modulation instability along the crest of the quasione- dimensional objects. As a model, we use coupled cubic quintic complex Ginzburg Landau equations. Among the final results found are stationary and oscillatory compound states as well as more complex assemblies consisting of quasi-one-dimensional and localized states. We analyse to what extent the final results can be described by the solutions of one cubic quintic complex Ginzburg Landau equation with effective parameters.

Original languageEnglish
Article number20150115
JournalPhilosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences
Volume373
Issue number2056
DOIs
StatePublished - 13 Dec 2015

Bibliographical note

Publisher Copyright:
© 2015 The Author(s) Published by the Royal Society. All rights reserved.

Keywords

  • Complex Ginzburg Landau equation
  • Dissipative solitons
  • Localized structures

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