Scattering of a two skyrmion configuration on potential holes or barriers in a model Landau-Lifshitz equation

The dynamics of a baby-skyrmion configuration, in a model Landau-Lifshitz equation, was studied in the presence of various potential obstructions. The baby-skyrmion configuration was constructed from two Q = 1 hedgehog solutions to the baby-skyrme model in (2+1) dimensions. The potential obstructions were created by introducing a new term into the Lagrangian which resulted in a localized inhomogeneity in the potential terms' coefficient. In the barrier system, the normal circular path was deformed as the skyrmions traversed the barrier. During the same period, it was seen that the skyrmions sped up as they went over the barrier. For critical values of the barrier height and width, the skyrmions were no longer bound and were free to separate. In the case of a potential hole, the baby skyrmions no longer formed a bound state and moved asymptotically along the axis of the hole. It is shown how to modify the definition of the angular momentum to include the effects of the obstructions, so that it is conserved