Soliton dynamics in a fractional complex Ginzburg-Landau model

TL;DR

This paper investigates the behavior of dissipative solitons in a fractional complex Ginzburg-Landau model, developing analytical approximations and analyzing how Levy index influences soliton stability and interactions.

Contribution

It introduces a variational approximation for fractional NLSE solitons and explores the impact of Levy index on soliton dynamics in fractional CGLE.

Findings

Stability domains depend on Levy index

In-phase soliton pairs merge into single pulses

Merger distance varies with Levy index

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.