2005/03/01 by F. Musso, Fabio Musso, Matteo Petrera +8
Chemistry · Mathematics · Physics and Astronomy · #Algebraic structures and combinatorial models #FOS: Physical sciences #Mathematical Physics (math-ph) #Molecular spectroscopy and chirality #Nonlinear Waves and Solitons #math-ph #math.MP
paper · pdf · doi:10.48550/arxiv.math-ph/0503002
15 pages, 2 figures
arxiv created 2005/03/01 · openalex publication_date 2005/03/01 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We consider a hierarchy of classical Liouville completely integrable models sharing the same (linear) r--matrix structure obtained through an N--th jet--extension of \mathfraksu(2) rational Gaudin models. The main goal of the present paper is the study of the integrable model corresponding to N=3, since the case N=2 has been considered by the authors in separate papers, both in the one--body case (Lagrange top) and in the n--body one (Lagrange chain). We now obtain a rigid body associated with a Lie--Poisson algebra which is an extension of the Lie--Poisson structure for the two--field top, thus breaking its semidirect product structure. In the second part of the paper we construct an integrable discretization of a suitable continuous Hamiltonian flow for the system. The map is constructed following the theory of Bäcklund transformations for finite--dimensional integrable systems developed by V.B. Kuznetsov and E.K. Sklyanin.