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

Abstract

We 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 pages

References in corpus (3)

• Scattering Theory for Jacobi Operators with Quasi-Periodic Background
• Inverse Scattering Transform for the Toda Hierarchy with Quasi-Periodic Background
• Scattering Theory for Jacobi Operators with Steplike Quasi-Periodic Background

Cited by in corpus (12)

• Rigorous asymptotics of a KdV soliton gas
• On the long time asymptotic behavior of the modified Korteweg de Vries equation with step-like initial data
• On the Cauchy Problem for the Korteweg-de Vries Equation with Steplike Finite-Gap Initial Data I. Schwartz-Type Perturbations
• Analytic bounds on transmission probabilities
• On the Cauchy Problem for the modified Korteweg-de Vries Equation with Steplike Finite-Gap Initial Data
• Inverse scattering theory for Schrödinger operators with steplike potentials
• Trace Formulas for Schroedinger Operators in Connection with Scattering Theory for Finite-Gap Backgrounds
• Scattering theory for Schrödinger operators on steplike, almost periodic infinite-gap backgrounds
• Scattering theory with finite-gap backgrounds: Transformation operators and characteristic properties of scattering data
• The Transformation Operator for One-Dimensional Schroedinger Operators on Almost Periodic Infinite-Gap Backgrounds
• A Paley-Wiener Theorem for Periodic Scattering with Applications to the Korteweg-de Vries Equation
• Multichannel scattering for the Schrödinger equation on a line with different thresholds at both infinities