Bogomolny equations for the BPS Skyrme models with impurity

TL;DR

This paper demonstrates how the BPS Skyrme model and its baby version can be coupled with impurities while preserving BPS properties, deriving the corresponding Bogomolny equations.

Contribution

It introduces a method to couple impurities to BPS Skyrme models without breaking their BPS nature and derives the associated Bogomolny equations.

Findings

Coupling of impurities preserves BPS properties in Skyrme models

Derivation of Bogomolny equations for impurity-coupled models

Extension to (2+1) dimensional baby Skyrme models

Abstract

We show that the BPS Skyrme model, as well as its (2+1) dimensional baby version (restricted), can be coupled with an impurity in the BPS preserving manner. The corresponding Bogomolny equations are derived.