Dissipative solitons stabilized by nonlinear gradient terms: Time-dependent behavior and generic properties

• Type: Article in International Scientific Journal
• Date: 2022

Authors

Descalzi, O (Author) Other; Maria Inês Barbosa de Carvalho (Author) FEUP; Facao, M (Author) Other; Brand, HR (Author) Other

Journal

Title: Chaos

Vol. 32

ISSN: 1054-1500

Publisher: American Institute of Physics

Indexing

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Other information

Authenticus ID: P-00X-N86

DOI: 10.1063/5.0118348

Abstract (EN): We study the time-dependent behavior of dissipative solitons (DSs) stabilized by nonlinear gradient terms. Two cases are investigated: first, the case of the presence of a Raman term, and second, the simultaneous presence of two nonlinear gradient terms, the Raman term and the dispersion of nonlinear gain. As possible types of time-dependence, we find a number of different possibilities including periodic behavior, quasi-periodic behavior, and also chaos. These different types of time-dependence are found to form quite frequently from a window structure of alternating behavior, for example, of periodic and quasi-periodic behaviors. To analyze the time dependence, we exploit extensively time series and Fourier transforms. We discuss in detail quantitatively the question whether all the DSs found for the cubic complex Ginzburg-Landau equation with nonlinear gradient terms are generic, meaning whether they are stable against structural perturbations, for example, to the additions of a small quintic perturbation as it arises naturally in an envelope equation framework. Finally, we examine to what extent it is possible to have different types of DSs for fixed parameter values in the equation by just varying the initial conditions, for example, by using narrow and high vs broad and low amplitudes. These results indicate an overlapping multi-basin structure in parameter space. Published under an exclusive license by AIP Publishing.

Language: English

Type (Professor's evaluation): Scientific

No. of pages: 14