Inverse scattering theory for Schrödinger operators with steplike potentials
arXiv:1510.01835 · doi:10.15407/mag11.02.123
Abstract
We study the direct and inverse scattering problem for the one-dimensional Schrödinger 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.
28 pages