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

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

1995-03-10

arxiv.org/abs/hep-th/9503066v1

J.Math.Phys. 37 (1996) 3463-3482

Physics

High Energy Physics

High Energy Physics - Theory

25pp, LaTex

Scientific paper

10.1063/1.531575

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.

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