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INTEGRABLE THREE-BODY PROBLEMS WITH TWO- AND THREE-BODY INTERACTIONS

机译:具有两主体和三主体相互作用的不可整合的三主体问题

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Spin generalizations of both the elliptic Calogero-Marchioro-WoIfes model and the nonlinear Schrodinger model are studied. These models are three-body problems with two- and three-body potentials, and mathematically related with the exceptional root system of type G(2). We construct the integrable differential-difference operator, the so-called Dunkl operator, based on the infinite-dimensional representation for solutions of the variant of the classical Yang-Baxter equation. By use of these operators, we investigate the integrability and the scattering matrices. [References: 19]
机译:研究了椭圆Calogero-Marchioro-WoIfes模型和非线性Schrodinger模型的自旋推广。这些模型是具有两体和三体电势的三体问题,并且在数学上与类型G(2)的特殊根系相关。我们基于无穷维表示形式来构造经典Yang-Baxter方程变体的可解微分算子,即所谓的Dunkl算子。通过使用这些算子,我们研究了可积性和散射矩阵。 [参考:19]

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