Stationary problems for equation of the KdV type and dynamical r-matrices.
Abstract
We study a quite general family of dynamical r-matrices for an auxiliary loop algebra 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.
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