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Zapiski Nauchnykh Seminarov POMI, 2007, Volume 347, Pages 117–143 (Mi znsl77)  
On canonical variables for integrable models of magnets

E. Sh. Gutshabash

V. A. Fock Institute of Physics, Saint-Petersburg State University
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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 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.
Received: 15.07.2007
English version:
Journal of Mathematical Sciences (New York), 2008, Volume 151, Issue 2, Pages 2865–2879
DOI: https://doi.org/10.1007/s10958-008-9003-9
Bibliographic databases:
UDC: 517.9
Language: Russian
Citation: E. Sh. Gutshabash, “On canonical variables for integrable models of magnets”, Questions of quantum field theory and statistical physics. Part 20, Zap. Nauchn. Sem. POMI, 347, POMI, St. Petersburg, 2007, 117–143; J. Math. Sci. (N. Y.), 151:2 (2008), 2865–2879
Citation in format AMSBIB
\Bibitem{Gut07}
\by E.~Sh.~Gutshabash
\paper On canonical variables for integrable models of magnets
\inbook Questions of quantum field theory and statistical physics. Part~20
\serial Zap. Nauchn. Sem. POMI
\yr 2007
\vol 347
\pages 117--143
\publ POMI
\publaddr St.~Petersburg
\mathnet{http://mi.mathnet.ru/znsl77}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2458888}
\transl
\jour J. Math. Sci. (N. Y.)
\yr 2008
\vol 151
\issue 2
\pages 2865--2879
\crossref{https://doi.org/10.1007/s10958-008-9003-9}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-49249132723}
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