Relation between Backlund transformations and higher continuous symmetries of the Toda equation

In this paper we study one aspect of the continuous symmetries of the Toda equation. Namely, we establish a correspondence between Backlund transformations and continuous symmetries of the Toda equation. A symmetry transformation acting on a solution of the Toda equation can be seen as a superposition of Backlund transformations. Conversely, a Backlund transformation can be written, at least formally, as a composition of infinitely many higher symmetry transformations. This result reinforces the opinion that the presence of sufficiently many continuous symmetries for discrete equations is an indication of their integrability.