Three-dimensional solitons in ferrites and their stability

The study is made of soliton solution of nonlinear equations describing dynamics of some magnets as well as the field theory models. Three-dimensional solitons are analysed to which non-uniform magnetization precession corresponds. Necessary and sufficient conditions for soliton stability according to Lyapunov are obtained. The soliton without nodes is proved to be stable over a wide range of the precission frequencies and unstable beyond this range. Solitons with nodes are unstable at all frequencies.