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Discrete canonical system and non‐Abelian Toda lattice: Bäcklund–Darboux transformation, Weyl functions, and explicit solutions
Author(s) -
Sakhnovich A. L.
Publication year - 2007
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.200410506
Subject(s) - mathematics , abelian group , pure mathematics , toda lattice , eigenvalues and eigenvectors , iterated function , transformation (genetics) , lattice (music) , generating function , mathematical physics , algebra over a field , mathematical analysis , integrable system , quantum mechanics , acoustics , biochemistry , chemistry , physics , gene
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. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)