On the Lax pairs for the generalized Kowalewski and GoryachevChaplygin tops
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 $5\times 5$ matrix Lax pair for the deformed Kowalewski top is proposed. Also deformations of the twofield 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 SemenovTian {S}hansky. In addition, a similar deformation of the GoryachevChaplygin top and its $3\times 3$ matrix Lax representation is constructed.
 Publication:

arXiv eprints
 Pub Date:
 November 2001
 arXiv:
 arXiv:nlin/0111035
 Bibcode:
 2001nlin.....11035S
 Keywords:

 Nonlinear Sciences  Exactly Solvable and Integrable Systems
 EPrint:
 9 pages, LaTeX, with corrections