GBDT of discrete skew-selfadjoint Dirac systems and explicit solutions of the corresponding non-stationary problems

2017/12/16 by Alexander Sakhnovich
Mathematics · #math.CA #math.DS #msc:34A05 #msc:39A06 #msc:39A12

paper · pdf · doi:10.1007/978-3-030-04269-1\_15

published as Oper. Theory Adv. Appl. 271 (2018), pp. 535--557 · This paper is a certain prolongation of the papers arXiv:math/0410438 and arXiv:1501.00395

arxiv created 2017/12/16 · arxiv updated 2020/07/03

Abstract

Generalized Bäcklund-Darboux transformations (GBDTs) of discrete skew-selfadjoint Dirac systems have been successfully used for explicit solving of direct and inverse problems of Weyl-Titchmarsh theory. During explicit solving of the direct and inverse problems, we considered GBDTs of the trivial initial systems. However, GBDTs of arbitrary discrete skew-selfadjoint Dirac systems are important as well and we introduce these transformations in the present paper. The obtained results are applied to the construction of explicit solutions of the interesting related non-stationary systems.

Citations

• Discrete skew self-adjoint canonical system and the isotropic Heisenberg magnet model
• Skew‐selfadjoint Dirac systems with rational rectangular Weyl functions: explicit solutions of direct and inverse problems and integrable wave equations