Normal and anomalous random walks of 2-d solitons
arXiv:1803.08729 · doi:10.1063/1.5021586
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.
arXiv comment10 pages, 5 figures
References in corpus (6)
- Spatiotemporal mode-locking in multimode fiber lasers
- PyCUDA and PyOpenCL: A Scripting-Based Approach to GPU Run-Time Code Generation
- Random Time-Scale Invariant Diffusion and Transport Coefficients
- Dynamics of soliton explosions in passively mode-locked fiber lasers
- How to compare diffusion processes assessed by single-particle tracking and pulsed field gradient nuclear magnetic resonance
- Anomalous diffusion of dissipative solitons in the cubic-quintic complex Ginzburg-Landau equation in two spatial dimensions