Darboux-Moutard transformations and Poincare-Steklov operators
R.G. Novikov, I.A. Taimanov
TL;DR
This paper derives formulas connecting Poincare-Steklov operators for Schrödinger equations linked by Darboux-Moutard transformations, aiding in potential reconstruction from boundary measurements.
Contribution
It introduces formulas relating boundary operators for transformed Schrödinger equations, facilitating potential reconstruction algorithms.
Findings
Formulas relating Poincare-Steklov operators for Darboux-Moutard transformed equations.
Potential reconstruction algorithms can be tested using derived formulas.
Enhances understanding of boundary operator relations in inverse problems.
Abstract
Formulas relating Poincare-Steklov operators for Schroedinger equations related by Darboux-Moutard transformations are derived. They can be used for testing algorithms of reconstruction of the potential from measurements at the boundary.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsNonlinear Waves and Solitons · Advanced Mathematical Physics Problems · Algebraic and Geometric Analysis