Propagation of solitary waves in channels of decreasing depth
type: Item
instance of: scholarly article
title: Propagation of solitary waves in channels of decreasing depth
zbMATH Open document ID: 0625.76023
DOI: 10.1007/BF01008358
author: C. J. Knickerbocker
author: Alan C. Newell
published in: Journal of Statistical Physics
publication date: 1985-01-01T00:00:00Z
review text: The changes which occur in a right-going solitary wave as it travels a channel of decreasing depth are discussed. In addition to the changes in the solitary wave, we have found through a judicious use of the conservation laws two secondary structures (a shelf and a reflection). Each of these structures is small with respect to the solitary wave, though the mass flux associated with each is of the same order as that of the solitary wave. Of interest is that the amplitude of the reflected wave does not satisfy Green's law. But rather, the amplitude of the reflected wave is constant along left-going characteristics. This finding allows us to satisfy the mass flux conservation laws to leading order and establishes the perturbed Korteweg-de Vries equation as a consistent approximation for the right-going profile.
Mathematics Subject Classification ID: 76B25
Mathematics Subject Classification ID: 35Q99
Mathematics Subject Classification ID: 76M99
zbMATH DE Number: 4016431
zbMATH Keywords: solitary wave
zbMATH Keywords: conservation laws two secondary structures
zbMATH Keywords: Green's law
zbMATH Keywords: mass flux conservation laws
zbMATH Keywords: perturbed Korteweg-de Vries equation
MaRDI profile type: Publication
cites work: The solitary wave in water of variable depth
cites work: The solitary wave in water of variable depth. Part 2
cites work: On an asymptotic solution of the Korteweg–de Vries equation with slowly varying coefficients
cites work: Q5670314
cites work: Shelves and the Korteweg-de Vries equation
cites work: Reflections from solitary waves in channels of decreasing depth
cites work: Amplification and decay of long nonlinear waves
cites work: On the Korteweg—de Vries equation for a gradually varying channel
cites work: Long waves on a beach
full work available at URL: https://doi.org/10.1007/bf01008358
OpenAlex ID: W1986486439
description: scientific article; zbMATH DE number 4016431