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Long Nonlinear Waves in Resonance with Topography
Author(s) -
Choi Jongho,
Milewski Paul A.
Publication year - 2003
Publication title -
studies in applied mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.164
H-Index - 46
eISSN - 1467-9590
pISSN - 0022-2526
DOI - 10.1111/1467-9590.00229
Subject(s) - nonlinear system , slosh dynamics , physics , coupling (piping) , resonance (particle physics) , korteweg–de vries equation , scattering , surface wave , classical mechanics , initial value problem , mathematical analysis , mechanics , mathematics , optics , quantum mechanics , materials science , metallurgy
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 “sloshing” in a tank. Some three‐dimensional extensions are discussed.