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arXiv · 1501.00395

Skew-selfadjoint Dirac systems with rational rectangular Weyl functions: explicit solutions of direct and inverse problems and integrable wave equations

B. Fritzsche·M. A. Kaashoek·B. Kirstein·A. L. Sakhnovich
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Abstract

In this paper we study direct and inverse problems for discrete and continuous time skew-selfadjoint Dirac systems with rectangular (possibly non-square) pseudo-exponential potentials. For such a system the Weyl function is a strictly proper rational rectangular matrix function and any strictly proper rational matrix function appears in this way. In fact, extending earlier results, given a strictly proper rational matrix function we present an explicit procedure to recover the corresponding potential using techniques from mathematical system and control theory. We also introduce and study a nonlinear generalized discrete Heisenberg magnet model, extending earlier results for the isotropic case. A large part of the paper is devoted to the related discrete time systems of which the pseudo-exponential potential depends on an additional continuous time parameter. Our techniques allows us to obtain explicit solutions for the generalized discrete Heisenberg magnet model and evolution of the Weyl functions.

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B. Fritzsche, M. A. Kaashoek, B. Kirstein, A. L. Sakhnovich. 2015-01-02. Skew-selfadjoint Dirac systems with rational rectangular Weyl functions: explicit solutions of direct and inverse problems and integrable wave equations. https://doi.org/10.1002/mana.201500069

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