2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/174449We develop direct and inverse scattering theory for one-dimensional Schroedinger operators with steplike potentials which are asymptotically close to different finite-gap periodic potentials on different half-axes. We give a complete characterization of the scattering data, which allow unique solvability of the inverse scattering problem in the class of perturbations with finite second moment.34 pagesSpectral TheoryMathematical Physics34L25, 81U40; 34B30, 34L40text