The transition to explosive solitons and the destruction of invariant tori

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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.
Original languageAmerican English
Pages (from-to)660-668
Number of pages9
JournalCentral European Journal of Physics
Volume10
Issue number3
DOIs
StatePublished - 1 Jun 2012

Keywords

  • cubic-quintic Ginzburg-Landau equation
  • destruction of invariant tori
  • explosive dissipative solitons

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