Theoretical and Mathematical Physics

, Volume 131, Issue 1, pp 543–549 | Cite as

Lax Pairs for the Deformed Kowalevski and Goryachev–Chaplygin Tops

  • V. V. Sokolov
  • A. V. Tsiganov


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.


Integrable Case Similar Deformation Kirchhoff Equation Quadratic Deformation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 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. 2.
    V. V. Sokolov, Theor. Math. Phys., 129, 1335 (2001).Google Scholar
  3. 3.
    A. I. Bobenko, A. G. Reyman, and M. A. Semenov-Tian-Shansky, Commun. Math. Phys., 122, 321 (1989).Google Scholar
  4. 4.
    D. Markushevich, J. Phys. A, 34, 2125 (2001).Google Scholar
  5. 5.
    A. I. Bobenko and V. B. Kuznetsov, J. Phys. A, 21, 1999 (1988).Google Scholar
  6. 6.
    Yu. B. Suris, Phys. Lett. A, 180, 419 (1993).Google Scholar

Copyright information

© Plenum Publishing Corporation 2002

Authors and Affiliations

  • V. V. Sokolov
    • 1
  • A. V. Tsiganov
    • 2
  1. 1.Landau Institute for Theoretical PhysicsRAS, MoscowRussia
  2. 2.Department of Computational and Mathematical PhysicsSt. Petersburg State UniversitySt. PetersburgRussia

Personalised recommendations