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

摘要

A version of the iterated B\"acklund-Darboux transformation, where Darbouxmatrix takes a form of the transfer matrix function from the system theory, isconstructed for the discrete canonical system and Non-Abelian Toda lattice.Results on the transformations of the Weyl functions, insertion of theeigenvalues, and construction of the bound states are obtained. A wide class ofthe explicit solutions is given. An application to the semi-infinite blockJacobi matrices is treated.