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arXiv · hep-th/9308143

Linear $r$-Matrix Algebra for Systems Separable\\ in Parabolic Coordinates

J. C. Eilbeck·V. Z. Enol'skii·V. B. Kuznetsov·D. V. Leykin
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Abstract

We consider a hierarchy of many particle systems on the line with polynomial potentials separable in parabolic coordinates. Using the Lax representation, written in terms of $2\times 2$ matrices for the whole hierarchy, we construct the associated linear $r$-matrix algebra with the $r$-matrix dependent on the dynamical variables. A dynamical Yang-Baxter equation is discussed.

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J. C. Eilbeck, V. Z. Enol'skii, V. B. Kuznetsov, D. V. Leykin. 1993-08-30. Linear $r$-Matrix Algebra for Systems Separable\\ in Parabolic Coordinates. https://doi.org/10.1016/0375-9601(93)90697-x

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