Two-dimensional travelling waves over a moving bottom |
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Authors: | Shengfu Deng |
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Affiliation: | Institute of Applied Physics and Computational Mathematics, PO Box 8009, Beijing 100088, PR China |
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Abstract: | Two-dimensional travelling waves on an ideal fluid with gravity and surface tension over a periodically moving bottom with a small amplitude are studied. The bottom and the wave travel with a same speed. The exact Euler equations are formulated as a spatial dynamic system by using the stream function. A manifold reduction technique is applied to reduce the system into one of ordinary differential equations with finite dimensions. A homoclinic solution to the normal form of this reduced system persists when higher-order terms are added, which gives a generalized solitary wave—the homoclinic solution connecting a periodic solution. |
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Keywords: | 35J25 35J60 35Q35 76B15 76B25 |
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