Derivation and application of extended parabolic wave theories. I. The factorized Helmholtz equation

DOI10.1063/1.526149zbMath0551.76069OpenAlexW2052017428WikidataQ64005191 ScholiaQ64005191MaRDI QIDQ3343682

Louis Fishman, John J. McCoy

Publication date: 1984

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

Full work available at URL: https://doi.org/10.1063/1.526149

zbMATH Keywords

inverse problemacoustic propagation modelocean acousticoutgoing radiation conditionseismic studiesWeyl pseudodifferential equation

Mathematics Subject Classification ID

Hydro- and aero-acoustics (76Q05) Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05)

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Cites Work

• A parabolic approximation for elastic waves
• Bremmer series that correct parabolic approximations
• Calculus for Functions of Noncommuting Operators and General Phase-Space Methods in Quantum Mechanics. I. Mapping Theorems and Ordering of Functions of Noncommuting Operators
• On the determination of a differential equation from its spectral function
• Higher-order parabolic approximations to time-independent wave equations
• A path-integral approach to the parabolic approximation. I
• Directional spectral spreading in randomly inhomogeneous media
• On the elastic profiles of a layered medium from reflection data. Part I. Plane-wave sources
• On the elastic profiles of a layered medium from reflection data. Part II: Impulsive point source
• A Parabolic Theory of Stress Wave Propagation Through Inhomogeneous Linearly Elastic Solids
• Propagation through an anisotropic random medium
• Parabolic approximations for underwater sound propagation
• Helmholtz equation as an initial value problem with application to acoustic propagation
• Propagation of beamed signals through inhomogeneous media: A diffraction theory
• Relation between the solutions of the Helmhotz and parabolic equations for sound propagation
• Inverse scattering on the line
• The weyl calculus of pseudo-differential operators
• Caustic corrections using coherence theory
• Parabolic approximations to the time-independent elastic wave equation
• Applications of Function Space Integrals to Problems in Wave Propagation in Random Media
• The W.K.B. approximation as the first term of a geometric‐optical series