Elliptic solutions to Toda lattice hierarchy and elliptic Ruijsenaars-Schneider model
arXiv:2103.00214 · doi:10.1134/S0040577921080080
Abstract
We consider solutions of the 2D Toda lattice hierarchy which are elliptic functions of the zeroth time t_0=x. It is known that their poles as functions of t_1 move as particles of the elliptic Ruijsenaars-Schneider model. The goal of this paper is to extend this correspondence to the level of hierarchies. We show that the Hamiltonians which govern the dynamics of poles with respect to the m-th hierarchical times t_m and \bar t_m of the 2D Toda lattice hierarchy are obtained from expansion of the spectral curve for the Lax matrix of the Ruijsenaars-Schneider model at the marked points.
arXiv comment27 pages, no figures. arXiv admin note: text overlap with arXiv:1907.06621, arXiv:2102.03784
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