On the time-dependent parabolic wave equation
type: Item
instance of: scholarly article
title: On the time-dependent parabolic wave equation
zbMATH Open document ID: 1013.34059
DOI: 10.1155/S016117120210915X
author: Arthur D. Gorman
published in: International Journal of Mathematics and Mathematical Sciences
publication date: 2002-08-13T00:00:00Z
full work available at URL: https://eudml.org/doc/50056
full work available at URL: S016117120210915X.html
review text: Summary: One approach to the study of wave propagation in a restricted domain is to approximate the reduced Helmholtz equation by a parabolic wave equation. Here, the author considers the wave propagation in a restricted domain modelled by a parabolic wave equation whose properties vary both in space and in time. He develops a Wentzel-Kramers-Brillouin (WKB) formalism to obtain an asymptotic solution in noncaustic regions and modifies the Lagrange manifold formalism to obtain an asymptotic solution near caustics. Associated wave phenomena are also considered.
Mathematics Subject Classification ID: 34E20
Mathematics Subject Classification ID: 35J05
zbMATH DE Number: 1780424
zbMATH Keywords: wave propagation
zbMATH Keywords: reduced Helmholtz equation
zbMATH Keywords: parabolic wave equation
zbMATH Keywords: Wentzel-Kramers-Brillouin formalism
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1780424