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Stability of some stationary solutions to the forced KdV equation with one or two bumps

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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https://hal.archives-ouvertes.fr/hal-00743482
Contributor : Francoise Cudennec <>
Submitted on : Friday, October 19, 2012 - 10:39:30 AM
Last modification on : Monday, February 15, 2021 - 10:39:44 AM

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Frédéric Chardard, Frédéric Dias, Hai Yen Nguyen, Jean-Marc Vanden-Broeck. Stability of some stationary solutions to the forced KdV equation with one or two bumps. Journal of Engineering Mathematics, Springer Verlag, 2011, 70 (1-3), pp.175-189. ⟨10.1007/s10665-010-9424-6⟩. ⟨hal-00743482⟩

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