Theoretical and Mathematical Physics

, Volume 141, Issue 1, pp 1329–1347 | Cite as

Factorization of the Loop Algebra and Integrable Toplike Systems

  • I. Z. Golubchik
  • V. V. Sokolov


With any Lie algebra of Laurent series with coefficients in a semisimple Lie algebra and its decomposition into a sum of the subalgebra consisting of the Taylor series and a complementary subalgebra, we associate a hierarchy of integrable Hamiltonian nonlinear ODEs. In the case of the so(3) Lie algebra, our scheme covers all classical integrable cases in the Kirchhoff problem of the motion of a rigid body in an ideal fluid. Moreover, the construction allows generating integrable deformations for known integrable models.

integrable nonlinear ODE Lax pair loop algebra 


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Copyright information

© Plenum Publishing Corporation 2004

Authors and Affiliations

  • I. Z. Golubchik
    • 1
  • V. V. Sokolov
    • 2
  1. 1.Bashkirian State Pedagogical UniversityUfaRussia
  2. 2.Landau Institute for Theoretical PhysicsMoscowRussia

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