Self-dual compact gauged baby skyrmions in a continuous medium

TL;DR

This paper explores self-dual solutions called compactons in a modified gauged baby Skyrme model with a $Z_2$ symmetry, analyzing their properties in different magnetic media through numerical solutions.

Contribution

It introduces a new self-dual gauged baby Skyrme model with a $Z_2$ symmetry and provides numerical solutions for compacton configurations in various media.

Findings

Compacton profiles vary with the medium.

Numerical solutions confirm existence of self-dual configurations.

Model extends understanding of topological solitons in magnetic media.

Abstract

We investigate the existence of self-dual configurations in the restricted gauged baby Skyrme model enlarged with a $Z_2$--symmetry, which introduces a real scalar field. For such a purpose, we implement the Bogomol'nyi procedure that provides a lower bound for the energy and the respective self-dual equations whose solutions saturate such a bound. Aiming to solve the self-dual equations, we specifically focused on a class of topological structures called compacton. We obtain the corresponding numerical solutions within two distinct scenarios, each defined by a scalar field, allowing us to describe different magnetic media. Finally, we analyze how the compacton profiles change when immersed in each medium.