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Article Dans Une Revue Journal of Engineering Mathematics Année : 2011

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

Résumé

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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Dates et versions

hal-00743482 , version 1 (05-02-2024)

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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, 2011, 70 (1-3), pp.175-189. ⟨10.1007/s10665-010-9424-6⟩. ⟨hal-00743482⟩
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