Integrable Deformations of Tops Related to the Algebra $so(p,q)$
Teoretičeskaâ i matematičeskaâ fizika, Tome 141 (2004) no. 1, pp. 24-37
We propose an integrable deformation of the known model of two interacting tops on the algebra $so(p,q)$. We consider particular cases including the generalized Lagrange and Kovalevskaya tops. We construct the Lax matrices and the corresponding classical $R$-matrices.
Keywords:
integrable systems, classical $R$-matrix, Kovalevskaya top.
@article{TMF_2004_141_1_a1,
author = {A. V. Tsiganov},
title = {Integrable {Deformations} of {Tops} {Related} to the {Algebra} $so(p,q)$},
journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
pages = {24--37},
year = {2004},
volume = {141},
number = {1},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/TMF_2004_141_1_a1/}
}
A. V. Tsiganov. Integrable Deformations of Tops Related to the Algebra $so(p,q)$. Teoretičeskaâ i matematičeskaâ fizika, Tome 141 (2004) no. 1, pp. 24-37. http://geodesic.mathdoc.fr/item/TMF_2004_141_1_a1/
[1] A. G. Reiman, M. A. Semenov-Tyan-Shanskii, Integriruemye sistemy. Teoretiko-gruppovoi podkhod, Regulyarnaya i khaoticheskaya dinamika, Izhevsk, 2003
[2] V. V. Sokolov, A. V. Tsyganov, TMF, 131:1 (2002), 118 | DOI | MR | Zbl
[3] I. V. Komarov, V. V. Sokolov, A. V. Tsiganov, J. Phys. A, 36 (2003), 8035 | DOI | MR | Zbl
[4] I. Z. Golubchik, V. V. Sokolov, Funkts. analiz i ego prilozh., 36:3 (2002), 9 | DOI | MR | Zbl
[5] A. I. Bobenko, A. G. Reyman, M. A. Semenov-Tian-Shansky, Commun. Math. Phys., 122 (1989), 321 | DOI | MR | Zbl
[6] I. D. Marshall, Commun. Math. Phys., 191 (1998), 723 | DOI | MR | Zbl