On the Lax pairs for the generalized Kowalewski and Goryachev-Chaplygin 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× 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 Shansky. In addition, a similar deformation of the Goryachev-Chaplygin top and its 3× 3 matrix Lax representation is constructed.
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