Thin-layer solutions to the Helmholtz equation in three dimensions

DOI10.1016/j.wavemoti.2022.103069OpenAlexW4307039013MaRDI QIDQ2685020

John R. Ockendon, Hilary Ockendon

Publication date: 17 February 2023

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

Full work available at URL: https://doi.org/10.1016/j.wavemoti.2022.103069

zbMATH Keywords

Helmholtz equationgeometrical opticsparabolic wave equation

Mathematics Subject Classification ID

Numerical analysis (65-XX) Partial differential equations (35-XX)

Uses Software

• DLMF

Cites Work

• Direction diagram of radiation in the problem of an inflection point of the boundary
• Problem of whispering gallery waves in a neighborhood of a simple zero of the effective curvature of the boundary
• Contour integral solutions of the parabolic wave equation
• Tangent ray diffraction and the pekeris caret function
• Thin-Layer Solutions of the Helmholtz and Related Equations
• Asymptotic solution of some diffraction problems
• Boundary layer problems in diffraction theory
• Curvilinear Co-ordinate Systems in which the Helmholtz Equation Separates
• On the Theory of Complex Rays
• Thin-layer solutions of the Helmholtz equation
• Searchlight asymptotics for high-frequency scattering by boundary inflection
• High‐frequency approximations to ellipsoidal wave functions
• Asymptotic expansions of solutions of (▽²+k²)u=0
• Scalar wave diffraction by tangent rays.
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