Skyrmion-like excitations in dynamical lattices

TL;DR

This paper develops discrete models of Skyrmions in nonlinear lattices, analyzing their stability, dynamics, and potential stabilization methods, thus extending the concept of Skyrmions to lattice systems.

Contribution

It introduces discrete Skyrmion analogs in 2D and 3D lattices, providing analytical stability limits and exploring their dynamics and stabilization.

Findings

Stable and unstable Skyrmion configurations identified

Analytical and numerical stability limits established

External potentials can stabilize Skyrmions

Abstract

We construct discrete analogs of Skyrmions in nonlinear dynamical lattices. The Skyrmion is built as a vortex soliton of a complex field, coupled to a dark radial soliton of a real field. Adjusting the Skyrmion ansatz to the lattice setting allows us to construct a "baby-Skyrmion" in two dimensions (2D) and extend it into the 3D case (1D counterparts of the Skyrmions are also found). Stability limits for these patterns are obtained analytically and verified numerically. The dynamics of unstable discrete Skyrmions is explored, and their stabilization by external potentials is discussed.