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Lax Pairs for the Deformed Kowalevski and Goryachev–Chaplygin Tops

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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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REFERENCES

  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).

  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 

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Authors and Affiliations

  1. Landau Institute for Theoretical Physics, RAS, Moscow, Russia

    V. V. Sokolov

  2. Department of Computational and Mathematical Physics, St. Petersburg State University, St. Petersburg, Russia

    A. V. Tsiganov

Authors
  1. V. V. Sokolov
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  2. A. V. Tsiganov
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Sokolov, V.V., Tsiganov, A.V. Lax Pairs for the Deformed Kowalevski and Goryachev–Chaplygin Tops. Theoretical and Mathematical Physics 131, 543–549 (2002). https://doi.org/10.1023/A:1015109904417

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  • DOI: https://doi.org/10.1023/A:1015109904417

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