Inverse Scattering Theory for Schrodinger Operators with Steplike Potentials

I. Egorova, Z. Gladka, T.L. Lange, G. Teschl
2015 Journal of Mathematical Physics, Analysis, Geometry  
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.
doi:10.15407/mag11.02.123 fatcat:nxuwym7qvvedjpawl256zep23a