The existence of Bogomolny decompositions for gauged baby Skyrme models

TL;DR

This paper derives Bogomolny decompositions for gauged baby Skyrme models in (2+0) dimensions, identifying conditions on potentials for these models, which aids in understanding their soliton solutions.

Contribution

It provides the first derivation of Bogomolny equations for both restricted and full gauged baby Skyrme models in (2+0) dimensions, including potential conditions.

Findings

Derived Bogomolny equations for gauged baby Skyrme models.

Identified potential conditions necessary for Bogomolny decompositions.

Enhanced understanding of soliton solutions in these models.

Abstract

The Bogomolny decompositions (Bogomolny equations) for the gauged baby Skyrme models: restricted and full one, in (2+0)-dimensions, are derived, for some general classes of the potentials. The conditions, which must be satisfied by the potentials, for each of these mentioned models, are also derived.