Lax Pairs for the Deformed Kowalevski and Goryachev–Chaplygin Tops
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We consider a quadratic deformation of the Kowalevski top. This deformation includes a new integrable case for the Kirchhoff equations recently found by one of the authors as a degeneration. A 5×5 matrix Lax pair for the deformed Kowalevski top is proposed. We also find similar deformations of the two-field Kowalevski gyrostat and the so(p,q) Kowalevski top. All our Lax pairs are deformations of the corresponding Lax representations found by Reyman and Semenov-Tian-Shansky. A similar deformation of the Goryachev–Chaplygin top and its 3×3 matrix Lax representation is also constructed.
KeywordsIntegrable Case Similar Deformation Kirchhoff Equation Quadratic Deformation
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- 1.V. V. Sokolov, “A generalized Kowalevski Hamiltonian and new integrable cases on e(3) and so(4),” in: Kowalevski Property (V. B. Kuznetsov, ed., to appear in CRM Proceedings and Lecture Notes), Am. Math. Soc. (2002); nlin.SI/0110022 (2001).Google Scholar
- 2.V. V. Sokolov, Theor. Math. Phys., 129, 1335 (2001).Google Scholar
- 3.A. I. Bobenko, A. G. Reyman, and M. A. Semenov-Tian-Shansky, Commun. Math. Phys., 122, 321 (1989).Google Scholar
- 4.D. Markushevich, J. Phys. A, 34, 2125 (2001).Google Scholar
- 5.A. I. Bobenko and V. B. Kuznetsov, J. Phys. A, 21, 1999 (1988).Google Scholar
- 6.Yu. B. Suris, Phys. Lett. A, 180, 419 (1993).Google Scholar