Inverse scattering theory for Schr\"odinger operators with steplike potentials
Spectral Theory
2017-08-04 v1 Mathematical Physics
math.MP
Abstract
We study the direct and inverse scattering problem for the one-dimensional Schr\"odinger equation with steplike potentials. We give necessary and sufficient conditions for the scattering data to correspond to a potential with prescribed smoothness and prescribed decay to their asymptotics. These results are important for solving the Korteweg-de Vries equation via the inverse scattering transform.
Cite
@article{arxiv.1510.01835,
title = {Inverse scattering theory for Schr\"odinger operators with steplike potentials},
author = {Iryna Egorova and Zoya Gladka and Till Luc Lange and Gerald Teschl},
journal= {arXiv preprint arXiv:1510.01835},
year = {2017}
}
Comments
28 pages