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chapterNo Access
EXACT THEORY OF EXISTENCE AND STABILITY FOR TWO- AND THREE-DIMENSIONAL SOLITARY WAVES
- SHU-MING SUN
Water Waves01 Apr 2010
Preview Abstract
This note discusses the recent development on the existence and stability of two-dimensional and three-dimensional gravity-capillary waves on water of finite-depth. The Korteweg-de Vries (KdV) equation is derived formally from the exact governing equations and the solitary-wave solutions are obtained. The recent results on the existence of solutions of the exact equations near the solitary-wave solutions of the KdV equation are presented and various two-and three-dimensional wave solutions are given. Then, the stability of these solutions using exact equations is discussed. The ideas and methods to obtain these results are briefly mentioned.

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