Factorization of the wave equation in a nonplanar stratified medium

DOI10.1063/1.528186zbMath0646.73012OpenAlexW2028119686MaRDI QIDQ3790736

Vaughan H. Weston

Publication date: 1988

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

Full work available at URL: https://doi.org/10.1063/1.528186

zbMATH Keywords

decompositionwave splittingscalar wave equationstratificationsinverse scattering problemfamily of nested C(sup 2)-surfacesincoming and outgoing wave conditionsone-dimensional time-dependent direct and inverse problemspotential type integral operatorstime-dependent single and double layer potential type

Mathematics Subject Classification ID

Inverse problems for PDEs (35R30) Inverse problems for waves in solid mechanics (74J25) Hyperbolic equations and hyperbolic systems (35L99) Boundary value and inverse problems for harmonic functions in two dimensions (31A25)

Related Items (11)

Wave splitting and the reflection operator for the wave equation in R3 ⋮ Inverse problem for the dissipative wave equation in a stratified half-space and linearization of the imbedding equations ⋮ Determination of the permittivity and conductivity in R3 using wave splitting of Maxwell’s equations ⋮ Time dependent direct and inverse electromagnetic scattering for the dispersive cylinder ⋮ Wave splitting in the time domain for a radially symmetric geometry ⋮ Factorization of the dissipative wave equation and inverse scattering ⋮ Frequency domain wave-splitting techniques for plane stratified bianisotropic media ⋮ Three-dimensional electromagnetic inverse scattering for biisotropic dispersive media ⋮ Uniqueness in a frequency-domain inverse problem of a stratified uniaxial bianisotropic medium. ⋮ An ill-posed problem of the continuation of transient data for a hyperbolic equation in a three-dimensional inhomogeneous half-space ⋮ ``The source problem -- Transient waves propagating from internal sources in non-stationary media

Cites Work

• Obtaining scattering kernels using invariant imbedding
• Direct and inverse scattering in the time domain via invariant imbedding equations
• On the Relation of Transmission-Line Theory to Scattering and Transfer
• Higher-order parabolic approximations to time-independent wave equations
• Derivation and application of extended parabolic wave theories. I. The factorized Helmholtz equation
• Layer-stripping solutions of multidimensional inverse scattering problems
• Factorization of the wave equation in higher dimensions

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