Scattering Theory for Jacobi Operators with Steplike Quasi-Periodic Background

Abstract

We develop direct and inverse scattering theory for Jacobi operators with steplike quasi-periodic finite-gap background in the same isospectral class. We derive the corresponding Gel'fand-Levitan-Marchenko equation and find minimal scattering data which determine the perturbed operator uniquely. In addition, we show how the transmission coefficients can be reconstructed from the eigenvalues and one of the reflection coefficients.

14 pages

References in corpus (4)

• On the inverse scattering problem for Jacobi matrices with the spectrum on an interval, a finite system of intervals or a Cantor set of positive length
• Scattering Theory for Jacobi Operators with Quasi-Periodic Background
• Inverse Scattering Transform for the Toda Hierarchy with Quasi-Periodic Background
• Trace Formulas in Connection with Scattering Theory for Quasi-Periodic Background

Cited by in corpus (6)

• Stability of the periodic Toda lattice under short range perturbations
• Soliton Solutions of the Toda Hierarchy on Quasi-Periodic Backgrounds Revisited
• Inverse Scattering Theory for One-Dimensional Schroedinger Operators with Steplike Periodic Potentials
• Stability of the Periodic Toda Lattice in the Soliton Region
• Inverse scattering transform for the Toda hierarchy with steplike finite-gap backgrounds
• Scattering theory with finite-gap backgrounds: Transformation operators and characteristic properties of scattering data