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).
Bibliographical noteFunding 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
- Dissipative solitons
- Ginzburg–Landau equation