Scattering by a Potential Using Hyperbolic Methods

DOI10.2307/2008470zbMath0692.65068OpenAlexW4238960660WikidataQ56483861 ScholiaQ56483861MaRDI QIDQ3034776

Alvin Bayliss, Cathleen Synge Morawetz, Yan-yan Li

Publication date: 1989

Full work available at URL: https://doi.org/10.2307/2008470

zbMATH Keywords

algorithmiteration methodboundary layerinverse scatteringpotential functionhyperbolic methods

Mathematics Subject Classification ID

Inverse problems for PDEs (35R30) Wave equation (35L05) Quantum scattering theory (81U99) Applications to the sciences (65Z05)

Related Items

Reconstruction of steplike potentials ⋮ Inverse backscattering ⋮ Fixed angle inverse scattering in the presence of a Riemannian metric ⋮ Uniqueness for the inverse fixed angle scattering problem ⋮ Fixed Angle Inverse Scattering for Sound Speeds Close to Constant ⋮ The inverse backscattering problem in three dimensions ⋮ Fixed Angle Inverse Scattering for Almost Symmetric or Controlled Perturbations ⋮ Inverse scattering with fixed observation angle data in 2D ⋮ Computational methods for some inverse scattering problems ⋮ Fixed Angle Scattering: Recovery of Singularities and Its Limitations ⋮ The fixed angle scattering problem with a first-order perturbation ⋮ The fixed angle scattering problem and wave equation inverse problems with two measurements ⋮ Recovering singularities of a potential from singularities of scattering data ⋮ Inverse backscattering in two dimensions

Cites Work

• The Gelfand-Levitan, the Marchenko, and the Gopinath-Sondhi integral equations of inverse scattering theory, regarded in the context of inverse impulse-response problems
• The One-Dimensional Inverse Problem of Reflection Seismology
• The Calculations of an Inverse Potential Problem
• Inverse scattering in a stratified medium
• Inverse scattering. II. Three dimensions
• Inverse scattering on the line