Planar Skyrmions: vibrational modes and dynamics

We study Skyrmion dynamics in a (2+1)-dimensional Skyrme model. The system contains a dimensionless parameter α, with α=0 corresponding to the O(3) sigma-model. If two Skyrmions collide head-on, then they can either coalesce or scatter-this depends on α and on the incident speed v, and is affected by transfer of energy to and from the internal vibrational modes of the Skyrmions. We classify these internal modes and compute their spectrum, for a range of values of α. In particular, we find that there is a fractal-like structure of scattering windows, analogous to those seen for kink-antikink scattering in 1+1 dimensions.