On canonical variables for integrable models of magnets

Three integrable models – the deformed Heisenberg, Landau–Lifschits and Ishimori magnets are written in terms of the stereographic projection. The Hamiltonians of these models are obtained and certain questions related to the existence of exact solutions are studied. In particular, the stability of solitions is studied for the Heisenberg marnet, simplest stationary solutions are obtained for the Landau–Lifschitz magnet, and Hamiltonians and topological charges are calculated for several known solutions of the Ishimori model.