Inverse scattering on the half-line for energy-dependent Schr\"{o}dinger equations
Spectral Theory
2020-07-13 v2 Mathematical Physics
math.MP
Abstract
In this paper, we study the inverse scattering problem for energy-dependent Schr\"{o}dinger 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
Keywords
Cite
@article{arxiv.2006.12284,
title = {Inverse scattering on the half-line for energy-dependent Schr\"{o}dinger equations},
author = {Rostyslav Hryniv and Stepan Manko},
journal= {arXiv preprint arXiv:2006.12284},
year = {2020}
}
Comments
15 pages