Inverse problems for self-adjoint Dirac systems: explicit solutions and stability of the procedure
arXiv:1508.07954 · doi:10.7153/oam-10-56
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.
The paper is dedicated to the memory of Leiba Rodman and his results on Riccatti equations are actively used in the proof of stability. The procedure to solve inverse problem, considered in the paper, is based on the article arXiv:1105.2013
Cited by in corpus (4)
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- Scattering for general-type Dirac systems on the semi-axis: 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
- GBDT and explicit solutions for the matrix coupled dispersionless equations (local and nonlocal cases)