Discrete canonical system and non-Abelian Toda lattice: Backlund-Darboux transformation and Weyl functions

Abstract

A version of the iterated Bäcklund-Darboux transformation, where Darboux matrix takes a form of the transfer matrix function from the system theory, is constructed for the discrete canonical system and Non-Abelian Toda lattice. Results on the transformations of the Weyl functions, insertion of the eigenvalues, and construction of the bound states are obtained. A wide class of the explicit solutions is given. An application to the semi-infinite block Jacobi matrices is treated.

Second version: Section on the explicit solutions and results on the bound states and insertion of eigenvalues are added, the presentation is slightly changed