Discrete skew self-adjoint canonical system and the isotropic Heisenberg magnet model

A discrete analog of a skew self-adjoint canonical (Zakharov–Shabat or AKNS) system with a pseudo-exponential potential is introduced. For the corresponding Weyl function the direct and inverse problem are solved explicitly in terms of three parameter matrices. As an application explicit solutions a...

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Bibliographic Details
Published in:Journal of functional analysis 2005-11, Vol.228 (1), p.207-233
Main Authors: Kaashoek, M.A., Sakhnovich, A.L.
Format: Article
Language:English
Subjects:
Controllability
Isotropic Heisenberg magnet model
Observability
Realization
Skew self-adjoint discrete canonical system
Spin sequence
Weyl function
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Summary:A discrete analog of a skew self-adjoint canonical (Zakharov–Shabat or AKNS) system with a pseudo-exponential potential is introduced. For the corresponding Weyl function the direct and inverse problem are solved explicitly in terms of three parameter matrices. As an application explicit solutions are obtained for the discrete integrable nonlinear equation corresponding to the isotropic Heisenberg magnet model. State–space techniques from mathematical system theory play an important role in the proofs.
ISSN:0022-1236
1096-0783
DOI:10.1016/j.jfa.2004.10.022