# BPS Submodels of The Generalized Skyrme Model and How to Find Them

## TL;DR

This paper classifies known BPS submodels of the generalized Skyrme model into three groups, derives their Bogomolny equations rigorously, and introduces new submodels and solutions using the BPS Lagrangian method.

## Contribution

It provides a systematic classification of BPS submodels, derives their Bogomolny equations rigorously, and discovers new submodels and solutions within the generalized Skyrme model.

## Key findings

- Classified BPS submodels into three groups based on derivative terms.
- Derived Bogomolny's equations for these submodels.
- Identified new BPS submodels and solutions.

## Abstract

Using the BPS Lagrangian method we show that all known BPS submodels of the generalized Skyrme model, with a particular ansatz for the fields content, can be devided into three groups based on the (effective) number of derivative-terms in the BPS submodels. We are able to derive rigorously the Bogomolny's equations of those BPS submodels. The resulting Bogomolny's equations, along with possible constraint equations, are in general forms in which some of the known BPS submodels may contain other possible non-trivial (non-vacuum) solutions then the ones found in the literature. Furthermore, we derive some other new BPS submodels of the generalized Skyrme model for each of the groups and some of them yield new solutions.