### Abstract

We consider a hierarchy of many particle systems on the line with polynomial potentials separable in parabolic coordinates. Using the Lax representation, written in terms of 2×2 matrices for the whole hierarchy, we construct the associated linear r-matrix algebra with the r-matrix dependent on the dynamical variables. A dynamical Yang-Baxter equation is discussed. © 1993.

Original language | English |
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Pages (from-to) | 208-214 |

Number of pages | 7 |

Journal | Physics Letters A |

Volume | 180 |

Issue number | 3 |

Publication status | Published - 6 Sep 1993 |

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## Cite this

Eilbeck, J. C., Enol'skii, V. Z., Kuznetsov, V. B., & Leykin, D. V. (1993). Linear r-matrix algebra for systems separable in parabolic coordinates.

*Physics Letters A*,*180*(3), 208-214.