Caustics of nonlinear waves
type: Item
instance of: scholarly article
title: Caustics of nonlinear waves
zbMATH Open document ID: 0645.35062
DOI: 10.1016/0165-2125(87)90031-X
author: John K. Hunter
author: Joseph B. Keller
published in: Wave Motion
publication date: 1987-01-01T00:00:00Z
review text: Geometrical optics expansions for solutions of first order hyperbolic conservation laws are derived. The emphasis lies on the derivation of expansions at caustics of the solution. It is shown that for moderately large amplitudes in the caustic region the linear theory for caustics suffices to approximate the solution accurately, whereas away from the caustic for such amplitudes a nonlinear geometric optic expansion is needed. This is due to the fact that the caustic region is small, which prevents disturbances generated by nonlinear terms to accumulate. Moreover, for somewhat stronger waves, for which linear theory does not suffice at caustics, a weakly nonlinear caustic theory is developed. The expansions in this paper are derived and presented carefully. Estimates for the difference between the exact solution and the approximate solution are not given.
Mathematics Subject Classification ID: 35L65
Mathematics Subject Classification ID: 35C20
Mathematics Subject Classification ID: 78A05
zbMATH DE Number: 4052148
zbMATH Keywords: Geometrical optics expansions
zbMATH Keywords: conservation laws
zbMATH Keywords: expansions at caustics
zbMATH Keywords: large amplitudes
MaRDI profile type: Publication
cites work: Weakly nonlinear high frequency waves
cites work: Q4151274
cites work: Nonlinear Cusped Caustics for Dispersive Waves
cites work: Boundary layer problems in diffraction theory
cites work: Uniform asymptotic expansions at a caustic
cites work: Ondes asymptotiques et approchees pour des systèmes d'équations aux dérivées partielles non linéaires
cites work: Resonantly Interacting, Weakly Nonlinear Hyperbolic Waves. II. Several Space Variables
cites work: REFLECTION AT A LAMINAR BOUNDARY LAYER OF A WEAK STEADY DISTURBANCE TO A SUPERSONIC STREAM, NEGLECTING VISCOSITY AND HEAT CONDUCTION
full work available at URL: 0165-2125(87)90031-x
OpenAlex ID: W1997812024
description: scientific article; zbMATH DE number 4052148