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Stationary problems for equation of the KdV type and dynamical $r$-matrices.

We study a quite general family of dynamical $r$-matrices for an auxiliary loop algebra ${\cal L}({su(2)})$ related to restricted flows for equations of the KdV type. This underlying $r$-matrix structure allows to reconstruct Lax representations and to find variables of separation for a wide set of the integrable natural Hamiltonian systems. As an example, we discuss the Henon-Heiles system and a quartic system of two degrees of freedom in detail.

preprint1995arXivOpen access
P. P. KulishS. Rauch-WojciechowskiA. V. Tsiganov
hep-th
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Open access3 authors1 topic
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P. P. KulishS. Rauch-WojciechowskiA. V. Tsiganov

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