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Published Online: 12 July 2018
Accepted: March 2018

Normal and anomalous random walks of 2-d solitons featured

Chaos 28, 075505 (2018); https://doi.org/10.1063/1.5021586
Jaime Cisternas1,a), Tony Albers2, and Günter Radons2
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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, is 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 nonmoving 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.

ACKNOWLEDGMENTS

This work was funded in part by the Chilean Science and Technology Commission (CONICYT) (Grant No. FR-1170460).

References
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  1. © 2018 Author(s). Published by AIP Publishing.

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