Nonlinear Sciences – Exactly Solvable and Integrable Systems
Scientific paper
2001-11-15
Nonlinear Sciences
Exactly Solvable and Integrable Systems
9 pages, LaTeX, with corrections
Scientific paper
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 $5\times 5$ 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 $3\times 3$ matrix Lax representation is constructed.
Sokolov Valentin V.
Tsiganov Andrey V.
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