The nonlinear dispersion of Rayleigh waves
type: Item
instance of: scholarly article
title: The nonlinear dispersion of Rayleigh waves
zbMATH Open document ID: 0602.76021
DOI: 10.1016/0167-2789(85)90016-8
author: David Parker
published in: Physica D
publication date: 1985-01-01T00:00:00Z
review text: The present paper shows, using Whitham's method [\textit{G. B. Whitham}, Proc. R. Soc. Lond., Ser. A 283, 238-261 (1965; Zbl 0125.442)] for analysing modulations of wavetrains, that gradual changes of amplitude and wavelength of these nonlinear Rayleigh waves propagate in a particularly simple manner. The loci of constant phase speed always propagate as a simple wave, with group velocity \(c_ G=G(c)\). The phase curves also are characteristic curves of the modulation equations. It is shown that these two properties are general properties of the modulation of waveforms having phase speed depending only on wave steepness. Such waveforms arise from physical systems with no intrinsic scales of length or time.
Mathematics Subject Classification ID: 76B15
Mathematics Subject Classification ID: 74J20
Mathematics Subject Classification ID: 74H45
zbMATH DE Number: 3972426
zbMATH Keywords: averaged variational principle
zbMATH Keywords: nonlinear amplitude dispersion
zbMATH Keywords: shock formation
zbMATH Keywords: Whitham's method
zbMATH Keywords: modulations of wavetrains
zbMATH Keywords: nonlinear Rayleigh waves
zbMATH Keywords: group velocity
zbMATH Keywords: wave steepness
zbMATH Keywords: intrinsic scales of length
MaRDI profile type: Publication
full work available at URL: 0167-2789(85)90016-8
OpenAlex ID: W1977644367
cites work: Q4151274
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description: scientific article; zbMATH DE number 3972426