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

Alexander Sakhnovich
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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.

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Alexander Sakhnovich. 2004-01-31. Discrete canonical system and non-Abelian Toda lattice: Backlund-Darboux transformation and Weyl functions. https://doi.org/10.1002/mana.200410506

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