Algebraic Extensions of Gaudin Models
Abstract
We perform a InönüWigner contraction on Gaudin models, showing how the integrability property is preserved by this algebraic procedure. Starting from Gaudin models we obtain new integrable chains, that we call Lagrange chains, associated to the same linear $r$matrix structure. We give a general construction involving rational, trigonometric and elliptic solutions of the classical YangBaxter equation. Two particular examples are explicitly considered: the rational Lagrange chain and the trigonometric one. In both cases local variables of the models are the generators of the direct sum of $N$ $\mathfrak{e}(3)$ interacting tops.
 Publication:

Journal of Nonlinear Mathematical Physics
 Pub Date:
 2005
 DOI:
 10.2991/jnmp.2005.12.s1.39
 arXiv:
 arXiv:nlin/0410016
 Bibcode:
 2005JNMP...12S.482M
 Keywords:

 Nonlinear Sciences  Exactly Solvable and Integrable Systems;
 Mathematical Physics
 EPrint:
 15 pages, corrected formulas