Inverse problems for self-adjoint Dirac systems: explicit solutions and stability of the procedure

TL;DR

This paper presents an explicit, stable method for recovering self-adjoint matrix Dirac systems from rational Weyl functions, utilizing GBDT transformations and Riccati equations.

Contribution

It introduces a novel explicit recovery procedure for self-adjoint Dirac systems and proves its stability, combining GBDT and Riccati equation techniques.

Findings

Explicit recovery procedure established

Stability of the procedure proved

Applicable to systems with discrete and continuous spectra

Abstract

A procedure to recover explicitly self-adjoint matrix Dirac systems on semi-axis (with both discrete and continuous components of spectrum) from rational Weyl functions is considered. Its stability is proved. GBDT version of Baecklund-Darboux transformation and various important results on Riccati equations are used for this purpose.