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

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

High Energy Physics - Theory 2016-09-06 v1

Authors: 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.

Keywords

dynamical r-matrix kdv type equations restricted flows lax representation separation of variables henon-heiles system integrable hamiltonian systems

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@article{arxiv.hep-th/9503066,
  title  = {Stationary problems for equation of the KdV type and dynamical $r$-matrices.},
  author = {P. P. Kulish and S. Rauch-Wojciechowski and A. V. Tsiganov},
  journal= {arXiv preprint arXiv:hep-th/9503066},
  year   = {2016}
}

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

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