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We study the magnon modes in the presence of a topological soliton in a 2dHeisenberg easy-axis ferromagnet. The problem of magnon scattering on thesoliton with arbitrary relation between the soliton radius R and the "magneticlength" Delta_0 is investigated for partial modes with different values of theazimuthal quantum numbers m. Truly local modes are shown to be present for allvalues of m, when the soliton radius is enough large. The eigenfrequencies ofsuch internal modes are calculated analytically on limiting case of a largesoliton radius and numerically for arbitrary soliton radius. It is demonstratedthat the model of an isotropic magnet, which admits an exact analyticalinvestigation, is not adequate even for the limit of small radius solitons,R<<Delta_0: there exists a local mode with nonzero frequency. We use the dataabout local modes to derive the effective equation of soliton motion; thisequation has the usual Newtonian form in contrast to the case of the easy-planeferromagnet. The effective mass of the soliton is found.Comment: 33 pages (REVTeX), 12 figures (EPS

Internal modes and magnon scattering on topological solitons in two-dimensional easy-axis ferromagnets