Symmetries of generalized soliton models and submodels on target space $S^2$

TL;DR

This paper analyzes the symmetries of various soliton models with target space $S^2$, revealing differences in symmetry properties between models like Baby Skyrme and Faddeev--Niemi.

Contribution

It systematically computes all symmetries of these models and their submodels using the prolongation method, highlighting differences in symmetry structures.

Findings

Baby Skyrme submodels have additional symmetries.

Faddeev--Niemi submodels lack extra symmetries.

Symmetry properties depend on the specific model.

Abstract

Some physically relevant non-linear models with solitons, which have target space $S^2$, are known to have submodels with infinitly many conservation laws defined by the eikonal equation. Here we calculate all the symmetries of these models and their submodels by the prolongation method. We find that for some models, like the Baby Skyrme model, the submodels have additional symmetries, whereas for others, like the Faddeev--Niemi model, they do not.