Solitons in a baby-Skyrme model with invariance under area-preserving diffeomorphisms

We study the properties of soliton solutions in an analogue of the Skyrme model in 2+1 dimensions whose Lagrangian contains the Skyrme term and the mass term, but no usual kinetic term. The model admits a symmetry under area-preserving diffeomorphisms. We solve the dynamical equations of motion analytically for the case of spinning isolated baryon-type solitons. We take fully into account the induced deformation of the spinning Skyrmions and the consequent modification of its moment of inertia to give an analytical example of related numerical behavior found by Piette, Schroers, and Zakrzewski. We solve the equations of motion also for the case of an infinite, open string, and a closed annular string. In each case, the solitons are of finite extent, so called ''compactons,'' being exactly the vacuum outside a compact region. We end with indications on the scattering of baby Skyrmions, as well as some considerations as the properties of solitons on a curved space.