Inverse scattering theory for one-dimensional Schrödinger operators with steplike finite-gap potentials

DOI10.1007/s11854-008-0050-4zbMath1175.47009arXiv0707.4632OpenAlexW3099843685WikidataQ57343874 ScholiaQ57343874MaRDI QIDQ1001392

Iryna Egorova, Gerald Teschl, Anne Boutet de Monvel-Berthier

Publication date: 17 February 2009

Published in: Journal d'Analyse Mathématique (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0707.4632

zbMATH Keywords

scattering theoryKorteweg-de Vries equationinverse scatteringfinite gap potential

Mathematics Subject Classification ID

KdV equations (Korteweg-de Vries equations) (35Q53) Inverse scattering problems in quantum theory (81U40) Scattering theory of linear operators (47A40)

Related Items

Trace Formulas for Schrödinger Operators in Connection with Scattering Theory for Finite-gap Backgrounds, Long-time asymptotics of perturbed finite-gap Korteweg-de Vries solutions, Scattering theory with finite-gap backgrounds: transformation operators and characteristic properties of scattering data, A remark on the inverse scattering problem for the perturbed Hill equation, Soliton asymptotics for the KdV shock problem via classical inverse scattering, A multiple scattering theory approach to solving the time-dependent Schrödinger equation with an asymmetric rectangular potential, Inverse scattering transform and soliton solutions for square matrix nonlinear Schrödinger equations with non-zero boundary conditions, The transformation operator for Schrödinger operators on almost periodic infinite-gap backgrounds, Dispersive estimate for the 1D Schrödinger equation with a steplike potential, On the Long-Time Asymptotic Behavior of the Modified Korteweg--de Vries Equation with Step-like Initial Data, Analytic bounds on transmission probabilities, Rigorous asymptotics of a KdV soliton gas, On the Cauchy problem for the Korteweg-de Vries equation with steplike finite-gap initial data. II: Perturbations with finite moments, Riemann-Hilbert problem for Camassa-Holm equation with step-like initial data

Cites Work

• Scattering theory for Jacobi operators with quasi-periodic background
• Sturm-Liouville operators and applications. Transl. from the Russian by A. Iacob
• Solutions of the Korteweg-de Vries equation with steplike initial data
• Scattering theory for systems with different spatial asymptotics on the left and right
• One-dimensional scattering theory for quantum systems with nontrivial spatial asymptotics
• Inverse scattering by a local impurity in a periodic potential in one dimension
• Scattering for step-periodic potentials in one dimension
• Solutions of the korteweg–devries equation with steplike initial profile
• Inverse scattering transform for the Toda hierarchy with quasi-periodic background
• The Toda lattice with step-like initial data. Soliton asymptotics
• Transformation Operator for Jacobi Matrices with Asymptotically Periodic Coefficients
• Inverse scattering by a local impurity in a periodic potential in one dimension. II
• Inverse scattering for step-periodic potentials in one dimension
• Scattering theory for Jacobi operators with a steplike quasi-periodic background
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item