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

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

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

2 Scopus citations


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.

Original languageEnglish
Article number123107
Issue number12
StatePublished - 1 Dec 2022

Bibliographical note

Funding Information:
O.D. acknowledges the support of FONDECYT (CL), No. 1200357, and Universidad de los Andes through FAI initiatives. The work by M.I.C. and M.F. is financed by National Funds through the Portuguese funding agency, FCT—Fundação para a Ciência e a Tecnologia—within Project Nos. UIDB/50014/2020, UIDB/50025/2020, UIDP/50025/2020, and LA/P/0037/2020. H.R.B. acknowledges the Deutsche Forschungsgemeinschaft (DE) for partial support of this work.

Publisher Copyright:
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