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We develop direct and inverse scattering theory for one-dimensionalSchroedinger operators with steplike potentials which are asymptotically closeto different finite-gap periodic potentials on different half-axes. We give acomplete characterization of the scattering data, which allow uniquesolvability of the inverse scattering problem in the class of perturbationswith finite second moment.

Inverse Scattering Theory for One-Dimensional Schroedinger Operators with Steplike Periodic Potentials