Soliton scattering in the O(3) model on a torus

TL;DR

This paper investigates the stability and scattering behavior of solitons in the O(3) model on a torus through numerical simulations, revealing instability issues, stabilization methods, and characteristic scattering phenomena.

Contribution

It demonstrates how adding a Skyrme term stabilizes solitons in the O(3) model on a torus and analyzes their scattering properties, providing new insights into soliton dynamics in this setting.

Findings

Solitons are inherently unstable on a torus without stabilization.

Adding a Skyrme term stabilizes solitons in the model.

Scattering at right angles is consistently observed.

Abstract

Using numerical simulations, the stability and scattering properties of the O(3) model on a two-dimensional torus are studied. Its solitons are found to be unstable but can be stabilized by the addition of a Skyrme term to the Lagrangian. Scattering at right angles with respect to the initial direction of motion is observed in all cases considered. The model has no solutions of degree one, so when a field configuration that resembles a soliton is considered, it shrinks to become infinitely thin. A comparison of these results with those of the model defined on the sphere is made.