Geodesic
Factorization of the Loop Algebra and Integrable Toplike Systems
Teoretičeskaâ i matematičeskaâ fizika, Tome 141 (2004) no. 1, pp. 3-23 Cet article a éte moissonné depuis la source Math-Net.Ru

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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, loop algebra.
Mots-clés : Lax pair 
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I. Z. Golubchik; V. V. Sokolov. Factorization of the Loop Algebra and Integrable Toplike Systems. Teoretičeskaâ i matematičeskaâ fizika, Tome 141 (2004) no. 1, pp. 3-23. http://geodesic.mathdoc.fr/item/TMF_2004_141_1_a0/

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