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

TL;DR

This paper extends the use of generalized Bäcklund-Darboux transformations to arbitrary discrete skew-selfadjoint Dirac systems, enabling explicit solutions for related non-stationary problems, advancing the analytical tools in spectral theory.

Contribution

It introduces GBDTs for arbitrary discrete skew-selfadjoint Dirac systems and applies them to construct explicit solutions of associated non-stationary systems.

Findings

Extended GBDTs to general systems

Constructed explicit solutions for non-stationary problems

Enhanced analytical methods in spectral theory

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.