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On the development of a solitary wave moving over an uneven bottom

Published online by Cambridge University Press:  24 October 2008

R. S. Johnson
R. S. Johnson
Affiliation:
School of Mathematics, University of Newcastle upon Tyne
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Abstract

The numerical and experimental results given in Madsen and Mei(16) are predicted using asymptotic methods and some knowledge of the Korteweg-de Vries (K-dV) equation. This is accomplished by first deriving, using formal asymptotic expansions, the K-dV equation valid over a variable depth. The depth is chosen, in the first instance, to slowly vary on the same scale as the initial (small) amplitude of the motion. The appropriate form of the Kd-V equation is then

where H(X,ξ) describes the surface profile and d(σX) is the changing depth. The rest of the paper is devoted to a study of this equation.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 73 , Issue 1 , January 1973 , pp. 183 - 203
Copyright
Copyright © Cambridge Philosophical Society 1973

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