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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
Article

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.

Keywords

Integrable Case Similar Deformation Kirchhoff Equation Quadratic Deformation 
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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

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