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Solitary Water Waves


Solitary wave approaching the beach in the lagoon of Molokai, Hawaii (photo by R.I. Odom)


Solitary waves in shallow water are usually described by the famous Korteweg-de Vries (KdV) equation.
We go beyond that and study the generalized version of this equation introduced by Fokas [A.S. Fokas,
Physica D87, 145 (1995)], which gives a more accurate description especially for large, fast waves.

We find that the solitary wave solutions of Fokas' equation (unlike those of the KdV equation) cannot grow
indefinitely but become unstable beyond a certain critical wave height, just as real water waves.

A second result, equally realistic, is that the solitary waves with increasing amplitude gradually lose the
characteristic "soliton" property of the KdV solutions. This means that two sizeable solitary waves when
they meet do not emerge from the collision unscathed.

See publications 76 and 81.

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