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 matrix Lax pair for the deformed Kowalewski top is proposed. Also deformations of the two-field Kowalewski gyrostat and the 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 matrix Lax representation is constructed.
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