From su(2) Gaudin Models to Integrable Tops

Abstract

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.

This is a contribution to the Vadim Kuznetsov Memorial Issue on Integrable Systems and Related Topics, published in SIGMA (Symmetry, Integrability and Geometry: Methods and Applications) at http://www.emis.de/journals/SIGMA/

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Cited by in corpus (5)

• Limits of Gaudin algebras, quantization of bending flows, Jucys--Murphy elements and Gelfand--Tsetlin bases
• 1+1 Gaudin Model
• Backlund transformations for the elliptic Gaudin model and a Clebsch system
• Bäcklund Transformations for the Kirchhoff Top
• An integrable discretization of the rational su(2) Gaudin model and related systems