dorsal/arxiv
View SchemaLinear r-Matrix Algebra for a Hierarchy of One-Dimensional Particle Systems Separable in Parabolic Coordinates
| Authors | J C Eilbeck, V Z Enol'skii, V B Kuznetsov, D V Leykin |
|---|---|
| Categories | |
| ArXiv ID | solv-int/9809008 |
| URL | https://arxiv.org/abs/solv-int/9809008 |
Abstract
We consider a hierarchy of many-particle systems on the line with polynomial potentials separable in parabolic coordinates. The first non-trivial member of this hierarchy is a generalization of an integrable case of the H\'enon-Heiles system. We give a Lax representation in terms of $2\times 2$ matrices for the whole hierarchy and construct the associated linear r-matrix algebra with the r-matrix dependent on the dynamical variables. A Yang-Baxter equation of dynamical type is proposed. Classical integration in a particular case is carried out and quantization of the system is discussed with the help of separation variables. This paper was published in the rary issues: Sfb 288 Preprint No. 110, Berlin and Nonlinear Mathematical Physics, {\bf 1(3)}, 275-294 (1994)
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"abstract": "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\\\u0027enon-Heiles\nsystem. We give a Lax representation in terms of $2\\times 2$ 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)",
"arxiv_id": "solv-int/9809008",
"authors": [
"J C Eilbeck",
"V Z Enol\u0027skii",
"V B Kuznetsov",
"D V Leykin"
],
"categories": [
"solv-int",
"nlin.SI"
],
"title": "Linear r-Matrix Algebra for a Hierarchy of One-Dimensional Particle Systems Separable in Parabolic Coordinates",
"url": "https://arxiv.org/abs/solv-int/9809008"
},
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