Building patterns by traveling vortices and dipoles in periodic dissipative media

TL;DR

This paper investigates how traveling vortices and dipoles in a 2D complex Ginzburg-Landau system with a cellular potential can generate and sustain complex patterns, including a Newton's cradle-like dynamical regime.

Contribution

It introduces a novel pattern-formation scenario driven by the hopping motion of localized modes in a dissipative medium with a periodic potential.

Findings

Traveling dipoles and vortices can generate extended patterns.

A Newton's cradle regime of multi-soliton chains is observed.

Pattern formation is controlled by the hopping dynamics in the cellular structure.

Abstract

We analyze pattern-formation scenarios in the two-dimensional (2D) complex Ginzburg-Landau (CGL) equation with the cubic-quintic (CQ) nonlinearity and a cellular potential. The equation models laser cavities with built-in gratings, which are used to stabilize 2D patterns. The pattern-building process is initiated by kicking a localized compound mode, in the form of a dipole, quadrupole, or vortex which is composed of four local peaks. The hopping motion of the kicked mode through the cellular structure leads to the generation of various extended patterns pinned by the structure. In the ring-shaped system, the persisting freely moving dipole hits the stationary pattern from the opposite side, giving rise to several dynamical regimes, with the pinned multi-soliton chain playing the role of the Newton's cradle (NC).