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

P. P. Kulish; S. Rauch-Wojciechowski; A. V. Tsiganov

doi:10.1063/1.531575

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arXiv · hep-th/9503066

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

P. P. Kulish·S. Rauch-Wojciechowski·A. V. Tsiganov

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Abstract

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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P. P. Kulish, S. Rauch-Wojciechowski, A. V. Tsiganov. 1995-03-10. Stationary problems for equation of the KdV type and dynamical $r$-matrices.. https://doi.org/10.1063/1.531575

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