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Shallow-water waves, the Korteweg-deVries equation and solitons

Published online by Cambridge University Press:  29 March 2006

N. J. Zabusky  and
C. J. Galvin
N. J. Zabusky
Affiliation:
Bell Telephone Laboratories, Whippany, N. J. 07981
C. J. Galvin
Affiliation:
U.S. Army Coastal Engineering Research Center Washington, D. C.
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Abstract

A comparison of laboratory experiments in a shallow-water tank driven by an oscillating piston and numerical solutions of the Korteweg-de Vries (KdV) equation show that the latter can accurately describe slightly dissipative wavepropagation for Ursell numbers (h1L2/h03) up to 800. This is an input-output experiment, where the initial condition for the KdV equation is obtained from upstream (station 1) data. At a downstream location, the number of crests and troughs and their phases (or relative locations within a period) agree quantitatively with numerical solutions. The crest-to-trough amplitudes disagree somewhat, as they are more sensitive to dissipative forces. This work firmly establishes the soliton concept as necessary for treating the propagation of shallow-water waves of moderate amplitude in a low-dissipation environment.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 47 , Issue 4 , 29 June 1971 , pp. 811 - 824
Copyright
© 1971 Cambridge University Press

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