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posted on 22.08.2006by Roger H.J. Grimshaw
Solitary water waves are long nonlinear waves that can propagate steadily over
long distances. They were first observed by Russell in 1837 in a now famous
report  on his observations of a solitary wave propagating along a Scottish
canal, and on his subsequent experiments. Some forty years later theoretical
work by Boussinesq  and Rayleigh  established an analytical model.
Then in 1895 Korteweg and de Vries  derived the well-known equation
which now bears their names. Significant further developments had to wait
until the second half of the twentieth century, when there were two parallel
developments. On the one hand it became realised that the Korteweg-de Vries
equation was a valid model for solitary waves in a wide variety of physical
contexts. On the other hand came the discovery of the soliton by Kruskal and
Zabusky , with the subsequent rapid development of the modern theory
of solitons and integrable systems.