INVERSE SCATTERING THEORY FOR ONE-DIMENSIONAL SCHRODINGER OPERATORS WITH STEPLIKE FINITE-GAP POTENTIALS

摘要

We develop direct and inverse scattering theory for one-dimensional Schrodinger operators with steplike potentials which are asymptotically close to different finite-gap potentials on different half-axes. We give a complete characterization of the scattering data, which allows unique solvability of the inverse scattering problem in the class of perturbations with finite second moment.