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On canonical variables in integrable models of magnets

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Abstract

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 problems related to the existence of exact solutions are studied. In particular, 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. Bibliography: 33 titles.

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Authors and Affiliations

  1. Institute Research for Physics, St.Petersburg State University, St.Petersburg, Russia

    E. Sh. Gutshabash

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  1. E. Sh. Gutshabash
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Correspondence to E. Sh. Gutshabash.

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Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 347, 2007, pp. 117–143.

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Gutshabash, E.S. On canonical variables in integrable models of magnets. J Math Sci 151, 2865–2879 (2008). https://doi.org/10.1007/s10958-008-9003-9

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