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

2004/10/20 by M. A. Kaashoek, Alexander Sakhnovich, A. L. Sakhnovich · 4 citations
Mathematics · Physics and Astronomy · #Nonlinear Photonic Systems #Nonlinear Waves and Solitons #Quantum chaos and dynamical systems #math-ph #math.MP #math.SP #msc:35Q51 #msc:35Q55 #msc:39A12 #nlin.SI

paper · pdf · doi:10.1016/j.jfa.2004.10.022

published as J. Funct. Anal. 228 (2005) 207-233

arxiv created 2004/10/20 · openalex publication_date 2005/09/29 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/02

Abstract

A discrete analog of a skew selfadjoint 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.

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