English

On the Lax pairs for the generalized Kowalewski and Goryachev-Chaplygin tops

Exactly Solvable and Integrable Systems 2007-05-23 v2

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 5×55\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)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 3×33\times 3 matrix Lax representation is constructed.

Keywords

Cite

@article{arxiv.nlin/0111035,
  title  = {On the Lax pairs for the generalized Kowalewski and Goryachev-Chaplygin tops},
  author = {Vladimir V. Sokolov and Andrey V. Tsiganov},
  journal= {arXiv preprint arXiv:nlin/0111035},
  year   = {2007}
}

Comments

9 pages, LaTeX, with corrections