Trace Formulas for Schroedinger Operators in Connection with Scattering Theory for Finite-Gap Backgrounds
arXiv:0902.3917 · doi:10.1007/978-3-7643-9994-8_7
Abstract
We investigate trace formulas for one-dimensional Schroedinger operators which are trace class perturbations of quasi-periodic finite-gap operators using Krein's spectral shift theory. In particular, we establish the conserved quantities for the solutions of the Korteweg-de Vries hierarchy in this class and relate them to the reflection coefficients via Abelian integrals on the underlying hyperelliptic Riemann surface.
14 pages
References in corpus (10)
- Non-self-adjoint operators, infinite determinants, and some applications
- Sum Rules and the Szego Condition for Orthogonal Polynomials on the Real Line
- Effective Pruefer Angles and Relative Oscillation Criteria
- Relative Oscillation Theory, Weighted Zeros of the Wronskian, and the Spectral Shift Function
- Stability of Periodic Soliton Equations under Short Range Perturbations
- Stability of the periodic Toda lattice under short range perturbations
- Inverse Scattering Theory for One-Dimensional Schroedinger Operators with Steplike Periodic Potentials
- On the Cauchy Problem for the modified Korteweg-de Vries Equation with Steplike Finite-Gap Initial Data
- Algebro-Geometric Constraints on Solitons with Respect to Quasi-Periodic Backgrounds
- Trace Formulas in Connection with Scattering Theory for Quasi-Periodic Background