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

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.

This paper is related to the paper arXiv:1508.07954 and deals with the case of discrete and continuous skew-selfadjoint Dirac systems (instead of the continuous selfadjoint case in arXiv:1508.07954). The discrete case is added in the current version

References in corpus (3)

• Discrete skew selfadjoint canonical systems 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
• Inverse problems for self-adjoint Dirac systems: explicit solutions and stability of the procedure

Cited by in corpus (4)

• Scattering for general-type Dirac systems on the semi-axis: reflection coefficients and Weyl functions
• Discrete Dirac systems on the semiaxis: rational reflection coefficients and Weyl functions
• General-type discrete self-adjoint Dirac systems: explicit solutions of direct and inverse problems, asymptotics of Verblunsky-type coefficients and stability of solving inverse problem
• On new classes of explicit solutions of Dirac, dynamical Dirac and Dirac--Weyl systems with non-vanishing at infinity potentials, their properties and applications