  We consider the baby Skyrme model in a physically motivated limit of reaching
the restricted or BPS baby Skyrme model, which is a model that enjoys
area-preserving diffeomorphism invariance. The perturbation consists of the
kinetic Dirichlet term with a small coefficient $\epsilon$ as well as the
standard pion mass term, with coefficient $\epsilon m_1^2$. The pions remain
lighter than the soliton for any $\epsilon$ and therefore the model is
physically acceptable, even in the $\epsilon \to 0$ limit. The version of the
BPS baby Skyrme model we use has BPS solutions with Gaussian tails. We perform
full numerical computations in the $\epsilon\to 0$ limit and even reach the
strict $\epsilon=0$ case, finding new nontrivial BPS solutions, for which we do
not yet know the analytic form.
