The transition to explosive solitons and the destruction of invariant tori

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...

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Bibliographic Details
Published inCentral European journal of physics Vol. 10; no. 3; pp. 660 - 668
Main Authors Cisternas, Jaime, Descalzi, Orazio, Cartes, Carlos
Format Journal Article
LanguageEnglish
Published Heidelberg SP Versita 01.06.2012
Versita
De Gruyter
Subjects
Biological and Medical Physics
Biophysics
cubic-quintic Ginzburg-Landau equation
destruction of invariant tori
Environmental Physics
explosive dissipative solitons
Geophysics/Geodesy
Physical Chemistry
Physics
Physics and Astronomy
Research Article
destruction of invariant tori
explosive dissipative solitons
cubic-quintic Ginzburg-Landau equation
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Summary: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.
ISSN:1895-1082
2391-5471
1644-3608
2391-5471
DOI:10.2478/s11534-012-0023-1