1998/09/02 by J. C. Eilbeck, Eilbeck, J C, V. Z. Enolski +5
Chemistry · Physics and Astronomy · #Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Physical sciences #Molecular spectroscopy and chirality #Nonlinear Photonic Systems #Nonlinear Waves and Solitons #Quantum chaos and dynamical systems
paper · pdf · doi:10.48550/arxiv.solv-int/9809008
openalex publication_date 1998/09/02 · openalex created_date 2019/06/27 · openalex updated_date 2026/07/28
We consider a hierarchy of many-particle systems on the line with polynomial\npotentials separable in parabolic coordinates. The first non-trivial member of\nthis hierarchy is a generalization of an integrable case of the H 'enon-Heiles\nsystem. We give a Lax representation in terms of 2\× 2 matrices for the\nwhole hierarchy and construct the associated linear r-matrix algebra with the\nr-matrix dependent on the dynamical variables. A Yang-Baxter equation of\ndynamical type is proposed. Classical integration in a particular case is\ncarried out and quantization of the system is discussed with the help of\nseparation variables. This paper was published in the rary issues: Sfb 288\nPreprint No. 110, Berlin and Nonlinear Mathematical Physics, bf 1(3),\n275-294 (1994)\n