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

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

2003-11-02

arxiv.org/abs/nlin/0311004v2

Math. Nachr. 280, No.5-6, 631-653 (2007)

Nonlinear Sciences

Exactly Solvable and Integrable Systems

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

Scientific paper

10.1002/mana.200410506

A version of the iterated B\"acklund-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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