Lax Pairs for the Deformed Kowalevski and Goryachev–Chaplygin Tops |
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| Authors: | Sokolov V V Tsiganov A V |
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| Institution: | (1) Landau Institute for Theoretical Physics, RAS, Moscow, Russia;(2) Department of Computational and Mathematical Physics, St. Petersburg State University, St. Petersburg, Russia |
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| Abstract: | 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. |
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