On Bogomolny equations in the Skyrme model

TL;DR

This paper introduces a novel decomposition of the minimal Skyrme model into three coupled BPS submodels using strong necessary conditions, each with its own Bogomolny equations, providing new insights into topological bounds.

Contribution

It presents a complete decomposition of the Skyrme model into BPS submodels, a novel approach using strong necessary conditions to analyze topological bounds.

Findings

Decomposition into three coupled BPS submodels.

Derivation of Bogomolny equations for each submodel.

Saturation of bounds when Bogomolny equations are satisfied.

Abstract

Using the concept of strong necessary conditions (CSNC), we derive a complete decomposition of the minimal Skyrme model into a sum of three coupled BPS submodels with the same topological bound. The bounds are saturated if corresponding Bogomolny equations, different for each submodel, are obeyed.