Applications of KdV
type: Item
instance of: scholarly article
title: Applications of KdV
zbMATH Open document ID: 0842.58044
DOI: 10.1007/BF00994625
published in: Acta Applicandae Mathematicae
publication date: 1995-08-27T00:00:00Z
review text: The Korteweg-de Vries equation has touched on so varied a range of topics in ``abstract'' mathematics that it may be easy to overlook its origins and continuing applications in the applied sciences. The present paper is a fascinating and concise review of many such. In spite of the plethora of other integrable equations brought to birth over the past thirty years, the KdV remains a paradigm not only for our understanding of integrability but for many facets of the asymptotic analysis of physical phenomena. The author reviews the subjects of surface gravity waves, internal oceanic solitons, the acoustics of bubbly liquids, voidage in fluidized beds, magma flow and conduit waves, the great red spot on Jupiter, plasma physics and electrical transmission lines. In each case he discusses both theory and the experimental data, giving a critical appraisal of the successes of KdV theory. The diagnosis is a healthy one. Even in a case like the great red spot, where substantial problems remain, it seems clear that the KdV will play a key role in the final picture.
reviewed by: Christopher Athorne
Mathematics Subject Classification ID: 37J35
Mathematics Subject Classification ID: 37K10
Mathematics Subject Classification ID: 35Q53
Mathematics Subject Classification ID: 37N99
zbMATH DE Number: 790790
zbMATH Keywords: asymptotic analysis
zbMATH Keywords: solitons
zbMATH Keywords: Korteweg-de Vries equation
zbMATH Keywords: integrable equations
zbMATH Keywords: surface gravity waves
zbMATH Keywords: internal oceanic solitons
author: D. G. Crighton
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf00994625
OpenAlex ID: W4231315966
description: scientific article; zbMATH DE number 790790