  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.
