Multisolitons in a Two-dimensional Skyrme Model

The Skyrme model can be generalised to a situation where static fields are maps from one Riemannian manifold to another. Here we study a Skyrme model where physical space is two-dimensional euclidean space and the target space is the two-sphere with its standard metric. The model has topological soliton solutions which are exponentially localised. We describe a superposition procedure for solitons in our model and derive an expression for the interaction potential of two solitons which only involves the solitons’ asymptotic fields. If the solitons have topological degree 1 or 2 there are simple formulae for their interaction potentials which we use to prove the existence of solitons of higher degree. We explicitly compute the fields and energy distributions for solitons of degrees between one and six and discuss their geometrical shapes and binding energies.