Symmetries of generalized soliton models and submodels on target spaceS2

Some physically relevant non-linear models with solitons, which have targetspace $S^2$, are known to have submodels with infinitly many conservation lawsdefined by the eikonal equation. Here we calculate all the symmetries of thesemodels and their submodels by the prolongation method. We find that for somemodels, like the Baby Skyrme model, the submodels have additional symmetries,whereas for others, like the Faddeev--Niemi model, they do not.Comment: 18 pages, one Latex fil