This article is cited in 16 papers

Factorization of the Loop Algebra and Integrable Toplike Systems

I. Z. Golubchik^a, V. V. Sokolov<sup>b

a</sup> Bashkir State Pedagogical University
^b L. D. Landau Institute for Theoretical Physics, Russian Academy of Sciences

Abstract: 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.

Keywords: integrable nonlinear ODE, Lax pair, loop algebra.

Received: 12.01.2004
Revised: 04.03.2004

DOI: 10.4213/tmf113

 English version: Theoretical and Mathematical Physics, 2004, 141:1, 1329–1347

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