Explicit Bäcklund transformations for multifield Schrödinger equations. Jordan generalizations of the Toda chain

Bäcklund transformations for multifield analogs of the nonlinear Schrödinger equation that correspond to unital Jordan algebras are found. These Bäcklund transformations are explicit invertible autotransformations and as a result they are very convenient for the construction of exact solutions. It is established that to these Bäcklund transformations there correspond integrable multifield discrete–differential equations that generalize the infinite Toda chain. A simple construction is given by means of which multifield analogs of the infinite Toda chain can be constructed from every unital Jordan algebra. New examples of such chains are given.