2007 / June Volume 2 No.2
A long wave approximation for capillary-gravity waves and the Kawahara equation
| Published Date |
2007 / June
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|---|---|
| Title | A long wave approximation for capillary-gravity waves and the Kawahara equation |
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| Keyword | |
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| Pagination | 179-220 |
| Abstract | The Kawahara equation is a higher-order Korteweg-de Vries equation with an additional fifth order derivative term. It was derived by Hasimoto as a model of capillary-gravity waves in an infinitely long canal over a
at bottom in a long wave regime when the Bond number is nearly one third. In this paper, we give a mathematically rigorous justication of this modeling and show that the solution of the Kawahara equation approximates that of
the full problem of capillary-gravity waves in an appropriate sense for a long time interval. We also consider the case where the bottom is not at and derive coupled Kawahara type equations whose solution approximates that of the full problem in that case.
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| AMS Subject Classification |
35Q35, 35Q53, 76B15, 76B45
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| Received |
2005-06-02
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