| Autor: |
Fritzsche, B., Kaashoek, M. A., Kirstein, B., Sakhnovich, A. L. |
| Rok vydání: |
2015 |
| Předmět: |
|
| Zdroj: |
Math. Nachr. 289 (2016) 1792-1819 |
| Druh dokumentu: |
Working Paper |
| DOI: |
10.1002/mana.201500069 |
| Popis: |
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. |
| Databáze: |
arXiv |
| Externí odkaz: |
|
