# Discrete BPS Skyrmions

## TL;DR

This paper introduces a discrete version of the BPS Skyrme model that supports time-dependent solutions, analyzing their stability and dynamics across different lattice spacings and potential parameters.

## Contribution

It presents a novel discrete analogue of the extended BPS Skyrme model capable of time-dependent solutions and explores their stability properties.

## Key findings

- Solutions can be long-lived under certain conditions
- Stability depends on lattice spacing and potential parameter {}
- Solutions exhibit potential instabilities but may be stable for specific parameter ranges

## Abstract

A discrete analogue of the extended Bogomolny-Prasad-Sommerfeld (BPS) Skyrme model that admits time-dependent solutions is presented. Using the spacing h of adjacent lattice nodes as a parameter, we identify the spatial profile of the solution and the continuation of the relevant branch of solutions over the lattice spacing for different values of the potential (free) parameter {\alpha}. In particular, we explore the dynamics and stability of the obtained solutions, finding that, while they generally seem to be prone to instabilities, for suitable values of the lattice spacing and for sufficiently large value of {\alpha}, they may be long-lived in direct numerical simulations.