Linear r-Matrix Algebra for Systems Separable\\ in Parabolic Coordinates
J. C. Eilbeck, V. Z. Enol'skii, V. B. Kuznetsov, D. V. Leykin
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× 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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