TY - JOUR
T1 - Dissipative solitons stabilized by nonlinear gradients in one spatial dimension
T2 - From deterministic to stochastic aspects, and a perspective
AU - Descalzi, Orazio
AU - Cartes, Carlos
N1 - 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
PY - 2022/11
Y1 - 2022/11
N2 - 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).
AB - 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).
KW - Dissipative solitons
KW - Ginzburg–Landau equation
KW - Ginzburg–Landau equation
KW - Dissipative solitons
UR - http://www.scopus.com/inward/record.url?scp=85138469130&partnerID=8YFLogxK
U2 - 10.1016/j.chaos.2022.112703
DO - 10.1016/j.chaos.2022.112703
M3 - Article
AN - SCOPUS:85138469130
SN - 0960-0779
VL - 164
JO - Chaos, Solitons and Fractals
JF - Chaos, Solitons and Fractals
M1 - 112703
ER -