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Open Physics

formerly Central European Journal of Physics

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Volume 10, Issue 3

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Volume 1 (2003)

The transition to explosive solitons and the destruction of invariant tori

Jaime Cisternas
  • Complex Systems Group, Facultad de Ingeniería y Ciencias Aplicadas, Universidad de los Andes, Av. San Carlos de Apoquindo, 2200, Santiago, Chile
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 / Orazio Descalzi
  • Complex Systems Group, Facultad de Ingeniería y Ciencias Aplicadas, Universidad de los Andes, Av. San Carlos de Apoquindo, 2200, Santiago, Chile
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 / Carlos Cartes
  • Complex Systems Group, Facultad de Ingeniería y Ciencias Aplicadas, Universidad de los Andes, Av. San Carlos de Apoquindo, 2200, Santiago, Chile
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Published Online: 2012-06-17 | DOI: https://doi.org/10.2478/s11534-012-0023-1

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Abstract

We investigate the transition to explosive dissipative solitons and the destruction of invariant tori in the complex cubic-quintic Ginzburg-Landau equation in the regime of anomalous linear dispersion as a function of the distance from linear onset. Using Poncaré sections, we sequentially find fixed points, quasiperiodicity (two incommesurate frequencies), frequency locking, two torus-doubling bifurcations (from a torus to a 2-fold torus and from a 2-fold torus to a 4-fold torus), the destruction of a 4-fold torus leading to non-explosive chaos, and finally explosive solitons. A narrow window, in which a 3-fold torus appears, is also observed inside the chaotic region.

Keywords: explosive dissipative solitons; cubic-quintic Ginzburg-Landau equation; destruction of invariant tori

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About the article

Published Online: 2012-06-17

Published in Print: 2012-06-01

Citation Information: Open Physics, Volume 10, Issue 3, Pages 660–668, ISSN (Online) 2391-5471, DOI: https://doi.org/10.2478/s11534-012-0023-1.

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© 2012 Versita Warsaw. This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License. BY-NC-ND 3.0

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