Normal and anomalous random walks of 2-d solitons

TL;DR

This paper investigates the complex behaviors of 2D solitons, including normal and anomalous random walks, caused by chaotic explosions modeled by the complex Ginzburg-Landau equation, using a novel statistical approach.

Contribution

It introduces a new analysis of soliton motion, revealing a sequence of normal and anomalous random walks during the transition from stationary to moving states.

Findings

Identification of a sequence of normal and anomalous random walks

Application of generalized diffusivities to characterize soliton dynamics

Insights into the transition mechanisms of soliton movement

Abstract

Solitons, which describe the propagation of concentrated beams of light through nonlinear media, can exhibit a variety of behaviors as a result of the intrinsic dissipation, diffraction, and the nonlinear effects. One of these phenomena, modeled by the complex Ginzburg-Landau equation, are chaotic explosions, transient enlargements of the soliton that may induce random transversal displacements, which in the long run lead to a random walk of the soliton center. As we show in this work, the transition from non-moving to moving solitons is not a simple bifurcation but includes a sequence of normal and anomalous random walks. We analyze their statistics with the distribution of generalized diffusivities, a novel approach that has been used successfully for characterizing anomalous diffusion.