Operator methods for inverse scattering on the real line

DOI10.1080/03605308508820393zbMath0585.35077OpenAlexW1977614958MaRDI QIDQ3710933

Anders Melin

Publication date: 1985

Published in: Communications in Partial Differential Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/03605308508820393

zbMATH Keywords

KdV equationpseudodifferential operatorscharacterization problemInverse scattering

Mathematics Subject Classification ID

Scattering theory for PDEs (35P25) Schrödinger operator, Schrödinger equation (35J10) Ordinary differential operators (34L99)

Related Items (32)

Inverse scattering for the 1-D Helmholtz equation ⋮ Asymptotic stability of solitons for mKdV ⋮ The asymptotic behavior of solutions of the Korteweg-de Vries equation evolving from very irregular data ⋮ Distribution of poles for scattering on the real line ⋮ Recovery of a potential from the ratio of reflection and transmission coefficients ⋮ Lieb-Thirring type inequality for resonances ⋮ Semiclassical estimates for scattering on the real line ⋮ Stability for the multifrequency inverse medium problem ⋮ Characterization of scattering data for the AKNS system ⋮ Certain inverse uniqueness from the quotients of scattering coefficients ⋮ Trace formulas for a complex KdV equation ⋮ Inverse scattering for the non-linear Schrödinger equation: Reconstruction of the potential and the non-linearity ⋮ \(L^p\)-\(L^{\acute p}\) estimates for the Schrödinger equation on the line and inverse scattering for the nonlinear Schrödinger equation with a potential ⋮ Energy Dependent Boundary Conditions and the Few-Body Scattering Problem ⋮ Structured matrix algorithms for inverse scattering on the line ⋮ Schrödinger operators in the twentieth century ⋮ Estimates of 1D resonances in terms of potentials ⋮ Reconstruction of the impedance Schrödinger equation from the modulus of the reflection coefficients ⋮ Inverse scattering with partial information on the potential ⋮ Properties of the scattering transform on the real line ⋮ Inverse Scattering for Schrödinger Operators with Miura Potentials, II. Different Riccati Representatives ⋮ Time-evolution-proof Scattering Data for the Focusing and Defocusing Zakharov-Shabat Systems ⋮ Sharp polynomial bounds on the number of scattering poles of radial potentials ⋮ KdV is well-posed in \(H^{-1}\) ⋮ Resonances in one dimension and Fredholm determinants ⋮ Inverse scattering on the line for the nonlinear Klein-Gordon equation with a potential ⋮ Stability of an Inverse Problem in Potential Scattering on The Real Line ⋮ The effect of a positive bound state on the KdV solution: a case study ^* ⋮ Inverse resonance scattering for Jacobi operators ⋮ Explicit construction of solutions of the modified Kadomtsev-Petviashvili equation ⋮ Inverse resonance problem with partial information on the interval ⋮ Direct scattering of AKNS systems with \(L^2\) potentials

Cites Work

• The spectrum of Hill's equation
• Inverse problem of quantum scattering theory. II
• Inverse scattering on the line
• Integrals of nonlinear equations of evolution and solitary waves

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