Discrete skew selfadjoint canonical systems and the isotropic Heisenberg magnet model

Details Discrete skew selfadjoint canonical systems and the isotropic Heisenberg magnet model Discrete skew selfadjoint canonical systems and the isotropic Heisenberg magnet model

2004-10-20

arxiv.org/abs/math/0410438v1

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

Mathematics

Spectral Theory

Scientific paper

10.1016/j.jfa.2004.10.022

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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