On the development of a solitary wave moving over an uneven bottom
- 1 January 1973
- journal article
- research article
- Published by Cambridge University Press (CUP) in Mathematical Proceedings of the Cambridge Philosophical Society
- Vol. 73 (1) , 183-203
- https://doi.org/10.1017/s0305004100047605
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 thenwhere 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.Keywords
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