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On the Lax pairs for the generalized Kowalewski and Goryachev-Chaplygin tops | | Vladimir V. Sokolov
; Andrey V. Tsiganov
; | | Date: |
15 Nov 2001 | | Subject: | Exactly Solvable and Integrable Systems | nlin.SI | | Affiliation: | Landau Institute for Theoretical Physics), Andrey V. Tsiganov (Department of Mathematical and Computational Physics of St.Petersburg University | | Abstract: | A polynomial deformation of the Kowalewski top is considered. This deformation includes as a degeneration a new integrable case for the Kirchhoff equations found recently by one of the authors. A $5 imes 5$ matrix Lax pair for the deformed Kowalewski top is proposed. Also deformations of the two-field Kowalewski gyrostat and the $so(p,q)$ Kowalewski top are found. All our Lax pairs are deformations of the corresponding Lax representations found by Reyman and Semenov-Tian {S}hansky. In addition, a similar deformation of the Goryachev-Chaplygin top and its $3 imes 3$ matrix Lax representation is constructed. | | Source: | arXiv, nlin.SI/0111035 | | Services: | Forum | Review | PDF | Favorites | |
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