DOI: 10.1063/5.0156518 ISSN:

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
  • Applied Mathematics
  • General Physics and Astronomy
  • Mathematical Physics
  • Statistical and Nonlinear Physics

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.

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