On the evolution of a solitary wave for very weak nonlinearity
- 12 July 1978
- journal article
- research article
- Published by Cambridge University Press (CUP) in Journal of Fluid Mechanics
- Vol. 87 (04) , 773-783
- https://doi.org/10.1017/s0022112078001883
Abstract
The initial-value problem for a one-dimensional gravity wave of amplitude a and characteristic length l in water of depth d is examined for 0 < a/d [Lt ] d2/l2 [Lt ] 1. A preliminary reduction leads to a Korteweg-de Vries (KdV) equation in which the nonlinear term is O(ε) relative to the linear terms, where ε = 3al2/4d3 [Lt ] 1 is a measure of nonlinearity/dispersion. The linear approximation (ε ↓ 0) is found to be valid if and only if .Keywords
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