Nonlinear dynamics and solitons in spin glasses

The properties of soliton solutions in a macroscopic model of a spin glass are investigated. A topological classification of the solitons is made. A study is made of the transformation properties and of the stability of two-parameter solitons to which there corresponds a localized precession of the spins with frequency $\omega$ in a frame of reference moving with the soliton with velocity ${\mathbf v}$. The parameters $\omega$ and ${\mathbf v}$ are related naturally to integrals of the motion of the solitons, namely, the number of magnons $N$ and the momentum $\mathbf P$. The stability of one-dimensional dynamical and topological solitons, and also three-dimensional solitons is studied on the basis of the theorems of Lyapunov and Chetaev.