Geodesic
Nonlinear dynamics of the magnetization of ferromagnets and motion of a generalized solid with flow group
Teoretičeskaâ i matematičeskaâ fizika, Tome 85 (1990) no. 1, pp. 115-123 Cet article a éte moissonné depuis la source Math-Net.Ru

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Arnol'd proposed an approach to investigation of the hydrodynamics of an ideal fluid based on the introduction of the group of diffeomorphisms of the flow region as configuration space. An analogous investigation was made of a generalized solid, the part of the configuration space being played by a certain Lie group. The motions were described by the geodesics of invariant metrics on the corresponding Lie groups [1]. The aim of the present paper is to apply such an approach to the problem of the nonlinear dynamics of the magnetization of ferromagnets. 
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V. A. Aleksovskii; A. M. Lukatskii. Nonlinear dynamics of the magnetization of ferromagnets and motion of a generalized solid with flow group. Teoretičeskaâ i matematičeskaâ fizika, Tome 85 (1990) no. 1, pp. 115-123. http://geodesic.mathdoc.fr/item/TMF_1990_85_1_a10/

[1] Arnold V., Annales de l'Institut Fourier, XVI:1 (1966), 319–361 | DOI | MR | Zbl

[2] Palais R. S., Foundation of Global Non-linear Analysis, Benjamin, New York–Amsterdam, 1968 | MR | Zbl

[3] Aleskovskii A. M., Stalmakhov V. S., Materialy 12 Vsesoyuznoi konferentsii po akustoelektronike i kvantovoi akustike (Saratov), IRE AN SSSR, M., 1983, 77–78

[4] Omori H., Lect. Notes in Math., 427, Springer-Verlag, Berlin–Heidelberg–New York, 1974 | DOI | MR | Zbl

[5] Dynkin E. B., UMN, 5:1 (1950), 135–186 | MR

[6] Ebin D. G., Marsden J., Annals of Math., 92:1 (1970), 102–163 | DOI | MR | Zbl

[7] Akhiezer A. I., Baryakhtar V. G., Peletminskii S. V., Spinovye volny, Nauka, M., 1967 | MR

[8] Gurevich A. G., Magnitnyi rezonans v ferritakh i antiferromagnetikakh, Nauka, M., 1973

[9] Barouch E., Fokas A. S., Papageorgiou V. G., J. Math. Phys., 29:12 (1988), 2628–2633 | DOI | MR | Zbl

[10] Braun U. F., Mikromagnetizm, Nauka, M., 1979

[11] Kosevich A. M., Ivanov B. A., Kovalev A. S., Nelineinye volny namagnichennosti. Dinamicheskie i topologicheskie solitony, Naukova dumka, Kiev, 1983

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

[13] Arnold V. I., Matematicheskie metody klassicheskoi mekhaniki, Nauka, M., 1974 | MR