Nonlinear Sciences – Exactly Solvable and Integrable Systems
Scientific paper
2007-12-11
Zapiski Nauchnych Seminarov POMI, v.347, 2007
Nonlinear Sciences
Exactly Solvable and Integrable Systems
20 pages
Scientific paper
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 - Lifschits magnet, and Hamiltonians and topological charges are calculated for several known solutions of the Ishimori model
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