Inverse scattering on the half-line for energy-dependent Schrödinger equations. (31st August 2020)

• Record Type: Journal Article
• Authors: Hryniv, Rostyslav O; Manko, Stepan S
• Is Part Of: Inverse problems. Volume 36:Number 9(2020)
• Publication Date: 2020-08-31
• Subjects: Schrödinger equation -- inverse scattering -- energy-dependent potentials; Inverse problems (Differential equations) -- Periodicals; 515.357
• DOI: 10.1088/1361-6420/aba416
• Languages: English
• ISSNs: 0266-5611

Abstract

Abstract: In this paper, we study the inverse scattering problem for energy-dependent Schrödinger equations on the half-line with energy-dependent boundary conditions at the origin. Under certain positivity and very mild regularity assumptions, we transform this scattering problem to the one for non-canonical Dirac systems and show that, in turn, the latter can be placed within the known scattering theory for ZS-AKNS systems. This allows us to give a complete description of the corresponding scattering functions S for the class of problems under consideration and justify an algorithm of reconstructing the problem from S .