  We study the dynamics of vortex-antivortex (VA) pairs in an infinitely thin
ferromagnetic film with easy-plane anisotropy. These are localized excitations
with finite energy that are characterized by a topological (skyrmion) number N
= 0,+1,-1. Topologically trivial (N=0) VA pairs undergo Kelvin motion analogous
to that encountered in fluid dynamics. In contrast, topologically nontrivial (N
= +1,-1) VA pairs perform rotational motion around a fixed guiding center. We
present the results of a detailed study in both cases and further demonstrate
that in the presence of dissipation a rotating N = +1,-1
  VA pair shrinks to a point and is annihilated, due to the discreteness of the
lattice, thus leading to a "topologically forbidden" (Delta N = 1) process. We
argue that the latter process underlies the experimentally observed vortex core
switching whereby the polarity of a single vortex is reversed after collision
with an N = 0 VA pair created by a burst of an applied alternating magnetic
field.
