BPS solitons with internal structures in a restricted baby Skyrme-Maxwell theory in a magnetic medium

TL;DR

This paper explores BPS solitons with internal ring-like structures in a modified baby Skyrme-Maxwell model incorporating magnetic permeability, deriving self-dual equations and numerically analyzing their solutions.

Contribution

It introduces a magnetic permeability-dependent potential in the baby Skyrme-Maxwell model and derives new self-dual equations with solutions exhibiting internal ring structures.

Findings

Self-dual equations depend on magnetic permeability.

Numerical solutions show concentric ring structures in magnetic fields.

Analytical explanation links structures to permeability parameters.

Abstract

We consider a restricted baby Skyrme-Maxwell scenario enlarged via the inclusion of a nontrivial magnetic permeability. We then proceed with the minimization of its total energy by means of the Bogomol'nyi-Prasad-Sommerfield (BPS) prescription, from which we get that the self-dual potential now depends on the magnetic permeability itself. As a result, we obtain not only the lower bound for the energy, but also the self-dual equations whose solutions saturate that bound. In such a context, we focus our attention on those time-independent gauged skyrmions with radial symmetry and no electric charge. We solve the effective self-dual equations numerically for different choices of the magnetic permeability, from which we obtain BPS magnetic fields whose internal structures form concentric rings. We also explain analytically the formation of these structures based on the values of a single real parameter which characterizes the respective magnetic permeabilities.