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

Abstract

Generalized B\"acklund-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.