Self-dual compactons in the gauged restricted baby Skyrme model in the presence of an external magnetic field

TL;DR

This paper explores the existence and properties of self-dual compact solitons in a gauged baby Skyrme model with external magnetic fields, analyzing different scenarios and solving the BPS equations numerically.

Contribution

It introduces a novel approach to implementing the BPS formalism in the presence of external magnetic fields and derives self-dual equations for compactons in this context.

Findings

Self-dual compactons can exist with external magnetic fields confined or encircling them.

Numerical solutions reveal how external fields influence compacton size and magnetic flux.

The study establishes the BPS bound and equations for these configurations.

Abstract

We investigate the existence of compact self-dual solitons in the restricted gauged baby Skyrme model in the presence of an external magnetic field. The consistent implementation of the Bogomol'nyi-Prasad-Sommerfield (BPS) formalism depends on the relative size between the compacton and the effective region occupied by the external magnetic field. To address this issue, we consider two scenarios: in the first, the external magnetic field is confined within the compacton, effectively playing the role of a magnetic impurity; in the second scenario, the external magnetic field fully encircles the compacton. For both cases, the approach has enabled us to set the self-dual potential, achieve the Bogomol'ny bound for the energy, and establish the self-dual or BPS equations whose solutions saturate such a bound. We next focused on obtaining radially symmetric compactons by solving the BPS system using two functions to describe the external magnetic field, a step-type function and a Gaussian function. After solving the BPS system numerically, we depicted the resulting field profiles and highlighted the effects induced on the compacton's size, field profiles, magnetic field, and magnetic flux.