Skyrmion-like states in two- and three-dimensional dynamical lattices.

Full Abstract

We construct, in discrete two-component systems with cubic nonlinearity, stable states emulating Skyrmions of the classical field theory. In the two-dimensional case, an analog of the baby Skyrmion is built on the square lattice as a discrete vortex soliton of a complex field [whose vorticity plays the role of the Skyrmion's winding number (WN)], coupled to a radial "bubble" in a real lattice field. The most compact quasi-Skyrmion on the cubic lattice is composed of a nearly planar complex-field discrete vortex and a three-dimensional real-field bubble; unlike its continuum counterpart which must have WN=2, this stable discrete state exists with WN=1. Analogs of Skyrmions in the one-dimensional lattice are also constructed. Stability regions for all these states are found in an analytical approximation and verified numerically. The dynamics of unstable discrete Skyrmions (which leads to the onset of lattice turbulence) and their partial stabilization by external potentials are explored too.

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Author information

Author/s: Kevrekidis, P G (PG); Carretero-González, R (R); Frantzeskakis, D J (DJ); Malomed, B A (BA); Diakonos, F K (FK);

Affiliation: Department of Mathematics and Statistics, University of Massachusetts, Amherst, Massachusetts 01003-4515, USA.

Journal and publication information

Publication Type: Journal Article

Journal: Physical review. E, Statistical, nonlinear, and soft matter physics (Phys Rev E Stat Nonlin Soft Matter Phys), published in United States. (Language: eng)

Reference: 2007-Feb; vol 75 (issue 2 Pt 2) : pp 026603

Dates: Created 2007/03/15; Completed 2007/04/20;

PMID: 17358432, status: PubMed-not-MEDLINE (last retrieval date: 12/26/2008)

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