Generalization of the Bremmer coupling series

DOI10.1063/1.531566zbMath0879.76088OpenAlexW2009775094MaRDI QIDQ5284788

Maarten V. de Hoop

Publication date: 22 January 1998

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

Full work available at URL: https://doi.org/10.1063/1.531566

zbMATH Keywords

convergenceexistencescattering problemwave operatorinteraction operatorpreferred directionhigh-frequency approximationdecomposition of acoustic wave fieldone-way ``parabolic approximation

Mathematics Subject Classification ID

Hydro- and aero-acoustics (76Q05) Initial value problems for first-order hyperbolic systems (35L45) Initial value problems for PDEs with pseudodifferential operators (35S10)

Related Items (8)

Modal expansion of one-way operators based on spectral differentiation matrix ⋮ Bremmer series for the multimodal sound propagation in inhomogeneous waveguides ⋮ Numerical factorization of propagation operator for hyperbolic equations and application to one-way, true amplitude one-way equations and Bremmer series ⋮ Asymptotic wave-splitting in anisotropic linear acoustics ⋮ Exact constructions of square-root Helmholtz operator symbols: The focusing quadratic profile ⋮ Generalization of the phase-screen approximation for the scattering of acoustic waves. ⋮ Reciprocity and representation theorems for flux- and field-normalised decomposed wave fields ⋮ Uniform high-frequency approximations of the square root Helmholtz operator symbol

Cites Work

• Numerical inversion of the Laplace transform: a survey and comparison of methods
• Wave propagation and the Bremmer series
• Phase space methods and path integration: the analysis and computation of scalar wave equations
• Pseudodifferential operators, operator orderings, marching algorithms and path integrals for one-way equations
• Scalar space-time waves in their spectral-domain first- and second-order Thiele approximations
• Invariant imbedding and generalizations of the WKB method and the Bremmer series
• The spectrum of positive elliptic operators and periodic bicharacteristics
• Bremmer series that correct parabolic approximations
• Elastic wave up/down decomposition in inhomogeneous and anisotropic media: An operator approach and its approximations
• Direct and inverse scattering in the time domain via invariant imbedding equations
• A new method of inversion of the Laplace transform
• A wide-angle split-step algorithm for the parabolic equation
• 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
• Factorization of the wave equation in higher dimensions
• Exact and operator rational approximate solutions of the Helmholtz, Weyl composition equation in underwater acoustics−The quadratic profile
• Invariant imbedding and wave splitting in R ³  : II. The Green function approach to inverse scattering
• The Feynman Integral

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