Anomalous diffusion of dissipative solitons in the cubic-quintic complex Ginzburg-Landau equation in two spatial dimensions

Abstract

We demonstrate the occurrence of anomalous diffusion of dissipative solitons in a `simple' and deterministic prototype model: the cubic-quintic complex Ginzburg-Landau equation in two spatial dimensions. The main features of their dynamics, induced by symmetric-asymmetric explosions, can be modeled by a subdiffusive continuous-time random walk, while in the case dominated by only asymmetric explosions it becomes characterized by normal diffusion.

arXiv comment6 pages, 6 figures

References in corpus (4)

• Random Time-Scale Invariant Diffusion and Transport Coefficients
• Observation of anomalous diffusion and fractional self-similarity in one dimension
• Time-averaged MSD of Brownian motion
• Persistent-random-walk approach to anomalous transport of self-propelled particles

Cited by in corpus (7)

• One-dimensional gap solitons in quintic and cubic-quintic Fractional nonlinear Schrödinger equations with a periodically modulated linear potential
• Impact of high-order effects on soliton explosions in the complex cubic-quintic Ginzburg-Landau equation
• Chaotic Diffusion in Delay Systems: Giant Enhancement by Time Lag Modulation
• Normal and anomalous random walks of 2-d solitons
• Anti-persistent random walks in time-delayed systems
• Chaotic Diffusion of Dissipative Solitons: From Anti-Persistent Random Walk to Hidden Markov Models
• Stepsize-adaptive integrators for dissipative solitons in cubic-quintic complex Ginzburg-Landau equations