Soliton dynamics in a fractional complex Ginzburg-Landau model

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 Schrodinger 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 Levy 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.

arXiv commentTo be published on Chaos, Solitons & Fractals

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• Localized modes in nonlinear fractional systems with deep lattices
• One-dimensional L{é}vy Quasicrystal
• Existence and Stability of Dissipative Solitons in a Dual-Waveguide Lattice with Linear Gain and Nonlinear Losses
• Propagation dynamics of abruptly autofocusing circular Airy-Gaussian vortex beams in the fractional Schrödinger equation
• Propagation dynamics of radially polarized symmetric Airy beams in the fractional Schrödinger equation