Nonlinear localized excitations in magnets with a weak exchange interaction as a soliton problem

Spin dynamics of soliton-like localized excitations in a discrete ferromagnetic chain with an easy-axis anisotropy and weak exchange interaction is studied. The relation of these excitations and dynamic magnetic solitons in the long-wave approximation is determined, and the dependence of frequency of localized excitations on the exchange interaction parameter for a fixed value of the total number of spin deviations is constructed. It is shown that this dependence is modified significantly for values of exchange interaction of the order of the one-ion anisotropy value.