On the evolution of packets of long surface waves
- 29 July 1975
- journal article
- Published by The Royal Society in Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences
- Vol. 344 (1638) , 427-433
- https://doi.org/10.1098/rspa.1975.0110
Abstract
Three dimensional inviscid nonlinear waves on the surface of water of finite depth are examined in the limit of long waves. It is shown that small amplitude waves having a suitably slow variation in the direction transverse to that of propagation satisfy a two dimensional analogue of the well known Korteweg-de Vries equation when the parameter Δ =ε /h 2 k 2 is finite; where ε is an amplitude parameter, h is the depth and k is the wavenumber. When Δ is small this analogue is reduced, to first approximation, to a scaled form of the nonlinear Schrödinger-Poisson type equations adumbrated by Davey & Stewartson (1974).Keywords
This publication has 2 references indexed in Scilit:
- On three-dimensional packets of surface wavesProceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences, 1974
- XLI. On the change of form of long waves advancing in a rectangular canal, and on a new type of long stationary wavesJournal of Computers in Education, 1895