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Discrete skew self-adjoint canonical system and the isotropic Heisenberg magnet model. (English) Zbl 1140.47311

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 systems theory play an important role in the proofs.

MSC:

47B39 Linear difference operators
37K15 Inverse spectral and scattering methods for infinite-dimensional Hamiltonian and Lagrangian systems
82B10 Quantum equilibrium statistical mechanics (general)
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