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

Abstract

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.