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On canonical variables for integrable models of magnets
Zapiski Nauchnykh Seminarov POMI, Questions of quantum field theory and statistical physics. Part 20, Tome 347 (2007), pp. 117-143 Cet article a éte moissonné depuis la source Math-Net.Ru

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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. 
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E. Sh. Gutshabash. On canonical variables for integrable models of magnets. Zapiski Nauchnykh Seminarov POMI, Questions of quantum field theory and statistical physics. Part 20, Tome 347 (2007), pp. 117-143. http://geodesic.mathdoc.fr/item/ZNSL_2007_347_a7/

[1] L. D. Landau, Sobranie trudov, Nauka, 1969, 128–143

[2] A. A. Belavin, A. M. Polyakov, Pisma v ZhETF, 22 (1975), 503–506

[3] A. M. Perelomov, UFN, 134 (1990), 577–609 | MR

[4] Yu. M. Izyumov, Yu. N. Skryabin, Statisticheskaya mekhanika magnitouporyadochennykh sistem, Nauka, 1987 | MR

[5] V. D. Lipovskii, A. V. Shirokov, Funkts. analiz i ego prilozh., 23:3 (1989), 65 | MR | Zbl

[6] O. I. Mokhov, Simplekticheskaya i puassonova geometriya na prostranstvakh petel gladkikh mnogoobrazii i integriruemye uravneniya, Institut Kompyuternykh issledovanii, Moskva–Izhevsk, 2004 | MR

[7] A. V. Mikhailov, A. I. Yaremchuk, Pisma v ZhETF, 36 (1982), 78

[8] S. P. Burtsev, V. E. Zakharov, A. V. Mikhailov, TMF, 70 (1987), 323 | MR | Zbl

[9] K. Porsezian, M. Lakshmanan, J. Math. Phys., 32 (1991), 2923 | DOI | MR | Zbl

[10] E. Sh. Gutshabash, Pisma v ZhETF, 73 (2001), 317–319

[11] E. K. Sklyanin, Preprint No E-3-79 LOMI, 1979

[12] A. I. Bobenko, Zap. nauchn. semin. LOMI, 123, 1983, 58 | MR | Zbl

[13] Niam-Ning Huang, Hao Cai and ot, arXiv: /nlin.SI/0509042

[14] B. G. Konopelchenko, Solitons in Multidimensions, World Scientific, 1993 | MR | Zbl

[15] E. Sh. Gutshabash, Zap. nauchn. semin. POMI, 291, 2002, 155–168 | MR | Zbl

[16] E. Sh. Gutshabash, Pisma v ZhETF, 78 (2003), 1257

[17] Qing Ding, arXiv: /math.DG/0504288 | MR

[18] A. N. Leznov, A. V. Razumov, J. Math. Phys., 35 (1994), 1738 | DOI | MR | Zbl

[19] E. V. Ferapontov, TMF, 91 (1992), 452 | MR

[20] V. G. Makhankov, Yu. P. Rybakov, V. I. Sanyuk, UFN, 162 (1994), 121–148 | DOI

[21] L. A. Takhtadzhyan, L. D. Faddeev, Gamiltonov podkhod v teopii solitonov, Nauka, M., 1986 | MR | Zbl

[22] E. Barouch, A. Fokas, V. Papageorgiou, J. Math. Phys., 29 (1988), 2628 | DOI | MR | Zbl

[23] E. M. Lifshits, L. P. Pitaevskii, Statisticheskaya fizika, Ch. 2, Nauka, M., 1978 | MR

[24] V. G. Baryakhtar, E. D. Belokolos, P. I. Golod, Sovremennye problemy teorii magnetizma, 30, Naukova dumka, Kiev, 1986

[25] V. M. Eleonskii, N. N. Kirova, N. E. Kulagin, ZhETF, 79 (1980), 321

[26] V. S. Mikhalev, Zap. nauchn. semin. LOMI, 189, 1991, 75–81 | Zbl

[27] E. Sh. Gutshabash, Zap. nauchn. semin. POMI, 335, 2006, 119–133 | MR | Zbl

[28] H. C. Fogedby, J. Phys. A: Math. Gen., 13 (1980), 1467–1499 | DOI | MR

[29] L. Martina, G. Profilo, G. Soliani, L. Solombrino, Phys. Rev. B, 49 (1994), 12915 | DOI

[30] R. Radzharaman, Solitony i instantony v kvantovoi teorii polya, Mir, M., 1985

[31] E. Sh. Gutshabash, V. D. Lipovskii, TMF, 90:2 (1992), 259 | MR | Zbl

[32] G. G. Varzugin, E. Sh. Gutshabash, V. D. Lipovskii, TMF, 104 (1995), 513 | MR | Zbl

[33] Y. Ishimori, Progr. Teor. Phys., 72 (1984), 33 | DOI | MR | Zbl