Exact and operator rational approximate solutions of the Helmholtz, Weyl composition equation in underwater acoustics−The quadratic profile

DOI10.1063/1.529666zbMath0755.76077OpenAlexW2066057938WikidataQ64005218 ScholiaQ64005218MaRDI QIDQ4020012

Louis Fishman

Publication date: 16 January 1993

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

Full work available at URL: https://doi.org/10.1063/1.529666

zbMATH Keywords

operator symbolsoperator rational approximationsWeyl pseudodifferential operator calculusdirect and inverse wave propagationrefractive index profile reconstructionwide-angle propagation

Mathematics Subject Classification ID

Path integrals in quantum mechanics (81S40) Hydro- and aero-acoustics (76Q05) Phase-space methods including Wigner distributions, etc. applied to problems in quantum mechanics (81S30)

Related Items

Generalization of the Bremmer coupling series ⋮ An invariant imbedding analysis of general wave scattering problems ⋮ A ‘‘compact Green function’’ approach to the time-domain direct and inverse problems for a stratified dissipative slab ⋮ Analysis of the Green’s function approach to one-dimensional inverse problems. I. One parameter reconstruction ⋮ A parabolic approximation method with application to global wave propagation ⋮ Scattering on small three-dimensional, nonspherically symmetric potentials ⋮ Exact constructions of square-root Helmholtz operator symbols: The focusing quadratic profile ⋮ Discrete transparent boundary conditions for wide angle parabolic equations in underwater acoustics ⋮ Uniform high-frequency approximations of the square root Helmholtz operator symbol

Cites Work

• Obtaining scattering kernels using invariant imbedding
• A Green's function approach to the determination of internal fields
• Phase space methods and path integration: the analysis and computation of scalar wave equations
• Global, uniform, asymptotic wave-equation solutions for large wavenumbers
• Bremmer series that correct parabolic approximations
• An algebra of pseudodifferential operators and the asymptotics of quantum mechanics
• Direct and inverse scattering in the time domain via invariant imbedding equations
• Fast wavelet transforms and numerical algorithms I
• 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
• Wave splitting and the reflection operator for the wave equation in R3
• Direct and inverse scattering in the time domain for a dissipative wave equation. I. Scattering operators
• Explicit time-dependent Schrodinger propagators
• Higher Order Paraxial Wave Equation Approximations in Heterogeneous Media
• The Square Root of a 2 × 2 Matrix
• The weyl calculus of pseudo-differential operators
• Mathematical Aspects of the Weyl Correspondence

This page was built for publication: Exact and operator rational approximate solutions of the Helmholtz, Weyl composition equation in underwater acoustics−The quadratic profile