# BPS submodels of the Skyrme model

## TL;DR

This paper demonstrates that the standard Skyrme model can be decomposed into two BPS submodels with first-order equations, providing insights into their solutions and implications for the rational map approximation.

## Contribution

It introduces a novel decomposition of the Skyrme model into two BPS submodels, revealing their independent solutions and generalizations.

## Key findings

- The Skyrme model can be expressed as a sum of two BPS submodels.
- Each BPS submodel admits nontrivial solutions independently.
- The decomposition offers new perspectives on the rational map approximation.

## Abstract

We show that the standard Skyrme model without pion mass term can be expressed as a sum of two BPS submodels, i.e., of two models whose static field equations, independently, can be reduced to first order equations. Further, these first order (BPS) equations have nontrivial solutions, at least locally. These two submodels, however, cannot have common solutions. Our findings also shed some light on the rational map approximation. Finally, we consider certain generalisations of the BPS submodels.