Elliptic solutions of the Toda lattice hierarchy and the elliptic Ruijsenaars–Schneider model

We consider solutions of the 2D Toda lattice hierarchy which are elliptic functions zeroth time t_0=x. It is known that their poles as t_1 move particles Ruijsenaars-Schneider model. The goal this paper to extend correspondence level hierarchies. show Hamiltonians govern dynamics with respect m-th hierarchical times t_m and \bar obtained from expansion spectral curve for Lax matrix model at marked points.