Characterization of time-dependence for dissipative solitons stabilized by nonlinear gradient terms: Periodic and quasiperiodic vs chaotic behavior

Orazio Descalzi*, M. Facão, Carlos Cartes, M. I. Carvalho, Helmut R. Brand

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

1 Scopus citations

Abstract

We investigate the properties of time-dependent dissipative solitons for a cubic complex Ginzburg-Landau equation stabilized by nonlinear gradient terms. The separation of initially nearby trajectories in the asymptotic limit is predominantly used to distinguish qualitatively between time-periodic behavior and chaotic localized states. These results are further corroborated by Fourier transforms and time series. Quasiperiodic behavior is obtained as well, but typically over a fairly narrow range of parameter values. For illustration, two examples of nonlinear gradient terms are examined: the Raman term and combinations of the Raman term with dispersion of the nonlinear gain. For small quintic perturbations, it turns out that the chaotic localized states are showing a transition to periodic states, stationary states, or collapse already for a small magnitude of the quintic perturbations. This result indicates that the basin of attraction for chaotic localized states is rather shallow.

Original languageEnglish
Article number083151
JournalChaos
Volume33
Issue number8
DOIs
StatePublished - 1 Aug 2023

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