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arXiv · 1803.08729

Normal and anomalous random walks of 2-d solitons

Jaime Cisternas·Tony Albers·Günter Radons
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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.

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Jaime Cisternas, Tony Albers, Günter Radons. 2018-03-23. Normal and anomalous random walks of 2-d solitons. https://doi.org/10.1063/1.5021586

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