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Stability of some stationary solutions to the forced KdV equation with one or two bumps |
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| Authors: | Fr??d??ric Chardard Fr??d??ric Dias Hai Yen Nguyen Jean-Marc Vanden-Broeck |
| Affiliation: | 1. UMPA, ENS Lyon (site Sciences), 46 all??e d??Italie, 69364, Lyon Cedex 07, France 2. CMLA, ENS Cachan, CNRS, PRES UniverSud, 61 Av. President Wilson, 94230, Cachan, France 3. School of Mathematical Sciences, University College Dublin, Belfield, Dublin 4, Ireland 4. Laboratoire de Physique des Oc??ans, IFREMER, BP 70, 29280, Plouzan??, France 5. Department of Mathematics, University College London, London, WC1E 6BT, UK |
| 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?Cde 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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