Q-ball scattering on barriers and holes in one and two spatial dimensions

We discuss various scattering properties of non-topological solitons, Q-balls, on potential obstructions in (1 + 1) and (2 + 1) dimensions. These obstructions, barriers and holes, are inserted into the potential of the theory via the coupling parameter, i.e. λ-tilde, that is effective only in a certain region of space. When λ-tilde>1 the obstruction is a barrier and when 0<λ-tilde<1 the obstruction is a hole. The dynamics of Q-balls on such obstructions in (1 + 1) dimensions is shown to be very similar to that of topological solitons provided that the Q-balls are stable. In (2 + 1) dimensions, numerical simulations have shown some differences from the dynamics of topological solitons. We discuss these differences in some detail