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

## TL;DR

This paper investigates the anomalous diffusion behavior of dissipative solitons in a two-dimensional cubic-quintic complex Ginzburg-Landau equation, revealing subdiffusive dynamics caused by symmetric explosions and normal diffusion with asymmetric explosions.

## Contribution

It demonstrates the occurrence of anomalous diffusion in dissipative solitons within a well-known nonlinear PDE model, linking explosion symmetry to diffusion type.

## Key findings

- Dissipative solitons exhibit anomalous diffusion due to symmetric explosions.
- Symmetric explosions lead to subdiffusive behavior modeled by a continuous-time random walk.
- Asymmetric explosions result in normal diffusion behavior.

## 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.