Riemann–Hilbert problem approach for two-dimensional flow inverse scattering

DOI10.1063/1.4896741zbMath1305.81133OpenAlexW2046432369MaRDI QIDQ2928114

Alexey D. Agaltsov, Roman G. Novikov

Publication date: 6 November 2014

Published in: Journal of Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1063/1.4896741

zbMATH Keywords

inverse probleminverse scattering problemreconstruction algorithmstime-harmonic wave equationnon-local Riemann-Hilbert problem

Mathematics Subject Classification ID

Scattering theory for PDEs (35P25) Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics (81Q05) Inverse problems for PDEs (35R30) Inverse scattering problems in quantum theory (81U40) PDEs in connection with quantum mechanics (35Q40) Hydro- and aero-acoustics (76Q05) Riemann-Hilbert problems in context of PDEs (35Q15) Systems of linear higher-order PDEs (35G35)

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Cites Work

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• Identification of a connection from Cauchy data on a Riemann surface with boundary
• Multidimensional inverse spectral problem for the equation \(-\Delta \psi -(v(x)-Eu(x))\psi =0\)
• Inverse scattering transform for the time dependent Schrödinger equation with applications to the KPI equation
• The inverse scattering transform for the time-dependent Schrödinger equation and Kadomtsev-Petviashvili equation
• Analogs of multisoliton potentials for the two-dimensional Schrödinger operator
• The inverse scattering problem on a fixed energy level for two- dimensional Schrödinger operator
• Inverse problem of quantum scattering theory. II
• Construction of a two-dimensional Schrödinger operator with given scattering amplitude at fixed energy
• Inverse scattering problem for the two-dimensional Schrödinger operator, the \({\bar\partial}\)-method and nonlinear equations
• Inverse scattering problem for the Schrödinger equation with magnetic potential at a fixed energy
• Global identifiability for an inverse problem for the Schrödinger equation in a magnetic field
• Transparent potentials at fixed energy in dimension two. Fixed-energy dispersion relations for the fast decaying potentials
• Inverse problem by Cauchy data on an arbitrary sub-boundary for systems of elliptic equations
• On the Inverse Scattering Transform for the Kadomtsev-Petviashvili Equation
• On the Inverse Scattering of the Time-Dependent Schrödinger Equation and the Associated Kadomtsev-Petviashvili (I) Equation
• On inverse scattering at a fixed energy for potentials with a regular behaviour at infinity
• Kadomtsev-Petviashvili Equation Revisited and Integrability in 4 + 2 and 3 + 1
• A multidimensional inverse problem in quantum and acoustic scattering
• An Inverse Problem for the Wave Equation with First Order Perturbation
• The $ \bar\partial$-equation in the multidimensional inverse scattering problem
• Two-dimensional vector flow inversion by diffraction tomography
• A stationary approach to inverse scattering for schrodinger operators with first order perturbation
• Geometric approach to inverse scattering for the Schrödinger equation with magnetic and electric potentials
• Monochromatic Reconstruction Algorithms for Two-dimensional Multi-channel Inverse Problems
• Inverse Scattering Problem for the Schrödinger Operator with External Yang–Mills Potentials in Two Dimensions at Fixed Energy
• Recovering a potential from Cauchy data in the two-dimensional case

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