From su(2) Gaudin Models to Integrable Tops

Details From su(2) Gaudin Models to Integrable Tops From su(2) Gaudin Models to Integrable Tops

2007-03-13

arxiv.org/abs/math-ph/0703044v2

SIGMA 3 (2007), 058, 14 pages

Physics

Mathematical Physics

This is a contribution to the Vadim Kuznetsov Memorial Issue on Integrable Systems and Related Topics, published in SIGMA (Sym

Scientific paper

10.3842/SIGMA.2007.058

In the present paper we derive two well-known integrable cases of rigid body dynamics (the Lagrange top and the Clebsch system) performing an algebraic contraction on the two-body Lax matrices governing the (classical) su(2) Gaudin models. The procedure preserves the linear r-matrix formulation of the ancestor models. We give the Lax representation of the resulting integrable systems in terms of su(2) Lax matrices with rational and elliptic dependencies on the spectral parameter. We finally give some results about the many-body extensions of the constructed systems.

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