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.