Relativistic Toda chain at root of unity III. Relativistic Toda chain hierarchy

Abstract

The hierarchy of the classical nonlinear integrable equations associated with relativistic Toda chain model is considered. It is formulated for the N-th powers of the quantum operators of the corresponding quantum integrable models. Following the ideas of the paper hep-th/9606144 it is shown how one can obtain such a system from 2D Toda lattice system. The reduction procedure is described explicitly. The soliton solutions for the relativistic Toda chain are constructed using results of solv-int/9304002 in terms of the rational tau-functions. The vanishing properties of these tau-functions are investigated.