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Three integrable models - the deformed Heisenberg, Landau - Lifschits andIshimori magnets are written in terms of the stereographic projection. TheHamiltonians of these models are obtained and certain questions related to theexistence of exact solutions are studied. In particular, the stability ofsolitions is studied for the Heisenberg marnet, simplest stationary solutionsare obtained for the Landau - Lifschits magnet, and Hamiltonians andtopological charges are calculated for several known solutions of the Ishimorimodel

On canonical variables in integrable models of magnets