Pseudodifferential operators, operator orderings, marching algorithms and path integrals for one-way equations

DOI10.1016/0165-2125(87)90030-8zbMath0649.35080OpenAlexW1989474676WikidataQ60712114 ScholiaQ60712114MaRDI QIDQ1105784

John J. McCoy, L. Neil Frazer

Publication date: 1987

Published in: Wave Motion (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0165-2125(87)90030-8

zbMATH Keywords

path integralsseismologyocean acousticsmarching algorithmselliptic wave propagationone-way wave theoryparabolic wave theory

Mathematics Subject Classification ID

Pseudodifferential operators as generalizations of partial differential operators (35S05) Path integrals in quantum mechanics (81S40) Hydro- and aero-acoustics (76Q05) Partial differential equations of mathematical physics and other areas of application (35Q99) Integral, integro-differential, and pseudodifferential operators (47Gxx)

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Generalization of the Bremmer coupling series ⋮ Another interpretation and derivation of one-way wave theories ⋮ Generalization of the phase-screen approximation for the scattering of acoustic waves. ⋮ Reciprocity and representation theorems for flux- and field-normalised decomposed wave fields

Cites Work

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• Derivation and application of extended parabolic wave theories. I. The factorized Helmholtz equation
• Derivation and application of extended parabolic wave theories. II. Path integral representations
• Finite-difference solution to the parabolic wave equation
• Homogenization and Smoothing: A Unified View of Two Derivations of Effective Property Theories and Extensions
• The weyl calculus of pseudo-differential operators