Abstract
Free-surface flows past submerged obstacles in a channel are considered. The fluid is assumed to be inviscid and incompressible and the flow to be irrotational. The first-order approximation of long nonlinear surface waves over one or two bumps results in a forced Korteweg–de Vries (fKdV) equation. Solutions of the stationary fKdV equation are constructed and their stability is studied, either analytically or numerically. These various solutions include solitary waves over a single bump, solitary waves with two humps over a double bump, table-top solutions over a double bump and fronts.
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Dedicated to our good friend, teacher and collaborator Ernie Tuck, who kindly invited us to visit Adelaide on several occasions. F. Dias and J.-M. Vanden-Broeck.
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Chardard, F., Dias, F., Nguyen, H.Y. et al. Stability of some stationary solutions to the forced KdV equation with one or two bumps. J Eng Math 70, 175–189 (2011). https://doi.org/10.1007/s10665-010-9424-6
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DOI: https://doi.org/10.1007/s10665-010-9424-6