Semitopological solitons in planar ferromagnets

We establish the existence of a finite-energy solitary wave in a two-dimensional planar ferromagnet which moves rigidly at any constant velocity v that is smaller than the magnon velocity c. The shape of the calculated soliton depends crucially on the relative magnitude of v and c. For v<<c, the soliton describes a widely separated vortex-antivortex pair undergoing Kelvin motion at a relative distance . There exists a crossover velocity v0 at which the vortex-antivortex character is lost and the energy-momentum dispersion develops a cusp. For v0<v<c, the soliton becomes a lump with no apparent topological features and solves the modified KP equation in the limit . We also describe briefly a similar calculation of a vortex ring in a three-dimensional planar ferromagnet. These results together with the analytically known one-dimensional kink provide an interesting set of semitopological solitons whose physical significance is yet to be explored.