Bogomolny equation for the BPS Skyrme model from the strong necessary conditions

TL;DR

This paper introduces a systematic method to derive the Bogomolny equation for the BPS Skyrme model, including a generalization for non-zero external pressure, using strong necessary conditions applicable to Skyrme-like theories.

Contribution

It provides a novel, systematic approach to derive Bogomolny equations for the BPS Skyrme model and extends it to cases with external pressure.

Findings

Derived the Bogomolny equation for the BPS Skyrme model.

Generalized the equation for non-zero external pressure.

Applicable method to any Skyrme-like theory.

Abstract

We present a systematic tool of derivation of the Bogomolny equation for the BPS Skyrme model. Furthermore, we find a generalization of the Bogomolny equation to the case corresponding with a non-zero value of the external pressure. The method is based on the concept of strong necessary conditions and can be applied to any Skyrme like theory.