The evolution of periodic long surface waves over a periodic bottom topography resonant with the waves is studied. Coupled Korteweg-de Vries equations are derived and describe the evolution in terms of interaction between right- and left-traveling waves. The coupling arises from the cumulative effect of wave scattering. We discuss the various conserved quantities of the system and compute solutions for the initial value problem and for the time-periodic problem of fluid "sloshing̊ in a tank. Some three-dimensional extensions are discussed.

Original languageEnglish
Pages (from-to)21-48
Number of pages28
JournalStudies in Applied Mathematics
Issue number1
Early online date14 Dec 2002
Publication statusPublished - 1 Jan 2003

ASJC Scopus subject areas

  • Applied Mathematics


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