Inverse scattering for the nonlinear Schrödinger equation II. Reconstruction of the potential and the nonlinearity in the multidimensional case

DOI10.1090/S0002-9939-01-06016-6zbMath0986.35125OpenAlexW1747072918MaRDI QIDQ2750861

Ricardo Weder

Publication date: 21 October 2001

Published in: Proceedings of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1090/s0002-9939-01-06016-6

zbMATH Keywords

uniquenessscattering operatorreconstruction of the potentials

Mathematics Subject Classification ID

Scattering theory for PDEs (35P25) Inverse problems for PDEs (35R30) NLS equations (nonlinear Schrödinger equations) (35Q55) Inverse scattering problems in quantum theory (81U40)

Related Items (22)

The scattering map determines the nonlinearity ⋮ Inverse problem for a nonlinear Helmholtz equation ⋮ The inverse scattering problem for Schrödinger and Klein-Gordon equations with a nonlocal nonlinearity ⋮ The direct and inverse scattering problem for the semilinear Schrödinger equation ⋮ Time-dependent method for non-linear Schrödinger equations in inverse scattering problems ⋮ Recovery of a spatially-dependent coefficient from the NLS scattering map ⋮ The \(L^{p}\)-\(L^{p'}\) estimate for the Schrödinger equation on the half-line ⋮ Nonlinear waves and dispersive equations. Abstracts from the workshop held June 26 -- July 2, 2022 ⋮ Stability estimates for the recovery of the nonlinearity from scattering data ⋮ Recovery of a cubic nonlinearity for the nonlinear Schrödinger equation ⋮ The matrix nonlinear Schrödinger equation with a potential ⋮ Inverse scattering problem for time dependent Hartree-Fock equations in the three-body case ⋮ Inverse Scattering for the Nonlinear Schrödinger Equation with the Yukawa Potential ⋮ Inverse scattering problems for the Hartree equation whose interaction potential decays rapidly ⋮ Partial recovery of potentials in generalized nonlinear Schrödinger equations on the line ⋮ TOPOLOGICAL EFFECTS IN QUANTUM MECHANICS AND HIGH VELOCITY ESTIMATES ⋮ Multidimensional inverse scattering for the nonlinear Klein-Gordon equation with a potential ⋮ INVERSE BORN APPROXIMATION FOR THE GENERALIZED NONLINEAR SCHRÖDINGER OPERATOR IN TWO DIMENSIONS ⋮ Inverse \(N\)-body scattering with the time-dependent Hartree-Fock approximation ⋮ Time-dependent methods in inverse scattering problems for the Hartree-Fock equation ⋮ Uniqueness on identification of cubic convolution nonlinearity ⋮ High-velocity estimates and inverse scattering for quantum N-body systems with Stark effect

Cites Work

• On small data scattering with cubic convolution nonlinearity
• Nonlinear scattering theory at low energy: Sequel
• Exponential bounds and absence of positive eigenvalues for N-body Schrödinger operators
• The \(W_{k,p}\)-continuity of the Schrödinger wave operators on the line
• Inverse scattering for the non-linear Schrödinger equation: Reconstruction of the potential and the non-linearity
• Decay estimates for Schrödinger operators
• Inverse scattering for the nonlinear schrodinger equation
• The geometrical approach to multidimensional inverse scattering
• The \(W^{k,p}\)-continuity of wave operators for Schrödinger operators
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