J. d'Analyse Math. 106:1, 271-316 (2008) [DOI: 10.1007/s11854-008-0050-4]

Inverse Scattering Theory for One-Dimensional Schrödinger Operators with Steplike Finite-Gap Potentials

Anne Boutet de Monvel, Iryna Egorova, and Gerald Teschl

We develop direct and inverse scattering theory for one-dimensional Schrödinger 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 allow unique solvability of the inverse scattering problem in the class of perturbations with finite second moment.

MSC2000: Primary 34L25, 81U40; Secondary 34B30, 34L40
Keywords: Inverse scattering, periodic background, steplike

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