Soliton dynamics in a fractional complex Ginzburg-Landau model

Yunli Qiu, Boris A. Malomed, Dumitru Mihalache, Xing Zhu, Li Zhang and Yingji He

Chaos, Solitons & Fractals, 2020, vol. 131, issue C

Abstract: The general objective of the work is to study dynamics of dissipative solitons in the framework of a one-dimensional complex Ginzburg-Landau equation (CGLE) of a fractional order. To estimate the shape of solitons in fractional models, we first develop the variational approximation for solitons of the fractional nonlinear Schrödinger equation (NLSE), and an analytical approximation for exponentially decaying tails of the solitons. Proceeding to numerical consideration of solitons in fractional CGLE, we study, in necessary detail, effects of the respective Lévy index (LI) on the solitons’ dynamics. In particular, dependence of stability domains in the model's parameter space on the LI is identified. Pairs of in-phase dissipative solitons merge into single pulses, with the respective merger distance also determined by LI.

Keywords: Fractional complex Ginzburg-Landau equation; Dissipative solitons; Effective diffusion (search for similar items in EconPapers)
Date: 2020
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Citations: View citations in EconPapers (18)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:131:y:2020:i:c:s0960077919304175

DOI: 10.1016/j.chaos.2019.109471

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