Inverse scattering for Schrödinger operators with Miura potentials: I. Unique Riccati representatives and ZS-AKNS systems

DOI10.1088/0266-5611/25/11/115007zbMath1181.35330arXiv0910.0636OpenAlexW2963532170MaRDI QIDQ3652574

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Publication date: 18 December 2009

Published in: Inverse Problems (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0910.0636

zbMATH Keywords

Schrödinger operators inverse scattering mKdV equation ZS-AKNS systems Miura potentials

Mathematics Subject Classification ID

Particular ordinary differential operators (Dirac, one-dimensional Schrödinger, etc.) (34L40) Inverse problems for PDEs (35R30) Inverse scattering problems in quantum theory (81U40) Scattering theory, inverse scattering involving ordinary differential operators (34L25) Algebras of operators on Banach spaces and other topological linear spaces (47L10)

Related Items (12)

Inverse scattering on the half-line for ZS-AKNS systems with integrable potentials ⋮ Scattering theory for Schrödinger operators with Bessel-type potentials ⋮ Strict domain monotonicity of the principal eigenvalue and a characterization of lower boundedness for the Friedrichs extension of four-coefficient Sturm–Liouville operators ⋮ Inverse scattering for impedance Schrödinger operators. I: Step-like impedance lattice ⋮ Discrete nonlinear Fourier transforms and their inverses ⋮ Transformation operators for impedance Sturm-Liouville operators on the line ⋮ Inverse resonance scattering for massless Dirac operators on the real line ⋮ Inverse scattering on the half-line for energy-dependent Schrödinger equations ⋮ Inverse resonance scattering for Dirac operators on the half-line ⋮ Reconstruction of the impedance Schrödinger equation from the modulus of the reflection coefficients ⋮ Inverse Scattering for Schrödinger Operators with Miura Potentials, II. Different Riccati Representatives ⋮ One smoothing property of the scattering map of the KdV on \(\mathbb{R}\)

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