Skew-selfadjoint Dirac systems: stability of the procedure of explicit solving the inverse problem

TL;DR

This paper investigates the stability of explicit inverse problem solutions for skew-selfadjoint Dirac systems, introducing new asymptotic results and employing advanced mathematical tools like GBDT and Riccati equations.

Contribution

It presents a stability analysis of explicit inverse problem procedures and new asymptotic properties of pseudo-exponential potentials for Dirac systems.

Findings

Stability of inverse problem procedures is established.

New asymptotic behaviors of pseudo-exponential potentials are proved.

Methods from system theory and algebraic Riccati equations are effectively applied.

Abstract

Procedures to recover explicitly discrete and continuous skew-selfadjoint Dirac systems on semi-axis from rational Weyl matrix functions are considered. Their stability is shown. Some new facts on asymptotics of pseudo-exponential potentials (i.e., of explicit solutions of inverse problems) are proved as well. GBDT version of Backlund-Darboux transformation, methods from system theory and results on algebraic Riccati equations are used for this purpose.