## Abstract

We discuss a self-dual form or the Bäcklund transformations for the continuous (in time variable) gl_{N} Ruijsenaars–Schneider model. It is based on the first order equations in N+M complex variables which include N positions of particles and M dual variables. The latter satisfy equations of motion of the gl_{M} Ruijsenaars–Schneider model. In the elliptic case it holds M=N while for the rational and trigonometric models M is not necessarily equal to N. Our consideration is similar to the previously obtained results for the Calogero–Moser models which are recovered in the non-relativistic limit. We also show that the self-dual description of the Ruijsenaars–Schneider models can be derived from complexified intermediate long wave equation with discrete Laplacian by means of the simple pole ansatz likewise the Calogero–Moser models arise from ordinary intermediate long wave and Benjamin–Ono equations.

Original language | English |
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Pages (from-to) | 550-565 |

Number of pages | 16 |

Journal | Nuclear Physics B |

Volume | 927 |

DOIs | |

Publication status | Published - Feb 2018 |