Soliton-Magnon Scattering in Two-Dimensional Isotropic Ferromagnets

It is studied the scattering of magnons by the 2d topological Belavin-Polyakov soliton in isotropic ferromagnet. Analytical solutions of the scattering problem are constructed: (i) exactly for any magnon wave vectors for the partial wave with the azimuthal number m=1 (translational mode), and (ii) in the long- and short-wave limits for the rest modes. The magnon mode frequencies are found for the finite size magnets. An effective equation of the soliton motion is constructed. The magnon density of states, connected with the soliton-magnon interaction, is found in a long-wave approximation.