B?cklund transformation for the first flows of the relativistic Toda hierarchy and associated properties

摘要

In this communication we study a class of one parameter dependent auto-B?cklund transformations for the first flow of the relativistic Toda lattice and also a variant of the usual Toda lattice equation. It is shown that starting from the Hamiltonian formalism such transformations are canonical in nature with a well defined generating function. The notion of spectrality is also analyzed and the separation variables are explicitly constructed.