Dissipative solitons stabilized by nonlinear gradients in one spatial dimension: From deterministic to stochastic aspects, and a perspective

Orazio Descalzi*, Carlos Cartes

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

3 Scopus citations

Abstract

The purpose of this article is twofold. Firstly, to investigate the formation of localized spatiotemporal chaos in the complex cubic Ginzburg–Landau equation including nonlinear gradient terms. We found a transition to spatiotemporal disorder via quasiperiodicity accompanied by the fact that incommensurate satellite peaks arise around the fundamental frequency and its harmonics. Secondly, we review the influence of multiplicative noise on stationary pulses stabilized by nonlinear gradients. Numerical simulations show surprising results that are explained analytically. We found that multiplicative noise can induce a velocity change of propagating dissipative solitons. This completes previous communications on the two issues addressed in O. Descalzi et al., (2019, 2021, 2022).

Original languageEnglish
Article number112703
JournalChaos, Solitons and Fractals
Volume164
DOIs
StatePublished - Nov 2022

Bibliographical note

Funding Information:
This review is largely based on recent joint theoretical work about dissipative solitons stabilized by nonlinear gradients terms developed by O. Descalzi, C. Cartes, J. Cisternas (Santiago, Chile), and H.R. Brand (Bayreuth, Germany). O.D. and C.C. wish to acknowledge the support of FONDECYT, Chile (CL), No. 1200357 and Universidad de los Andes, Chile through FAI initiatives. All authors approved the manuscript to be published

Publisher Copyright:
© 2022

Keywords

  • Dissipative solitons
  • Ginzburg–Landau equation

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