Three-dimensional Solitary Gravity-capillary Water Waves
نویسنده
چکیده
The existence of solitary-wave solutions to the three-dimensional water-wave problem with strong surface-tension effects is predicted by the KP-I model equation. The term solitary wave describes any solution which has a pulse-like profile in its direction of propagation, and the KP-I equation admits explicit solutions for three different types of solitary wave. A line solitary wave is spatially homogeneous in the direction transverse to its direction of propagation, while a periodically modulated solitary wave is periodic in the transverse direction. A fully localised solitary wave on the other hand decays to zero in all spatial directions. In this article we outline mathematical results which confirm the existence of all three types of solitary wave for the full gravity-capillary water-wave problem in its usual formulation as a free-boundary problem for the Euler equations.
منابع مشابه
Transversally periodic solitary gravity-capillary waves.
When both gravity and surface tension effects are present, surface solitary water waves are known to exist in both two- and three-dimensional infinitely deep fluids. We describe here solutions bridging these two cases: travelling waves which are localized in the propagation direction and periodic in the transverse direction. These transversally periodic gravity-capillary solitary waves are foun...
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