Exact Theory of Three-Dimensional Water Waves at the Critical Speed

The paper concerns three-dimensional (3D) traveling gravity-capillary waves in water of finite depth. It was well known that the waves are determined by two constants: nondimensional wave speed F (called Froude number) and nondimensional surface tension b (called Bond number). For two-dimensional (2...

Full description

Saved in:
Bibliographic Details
Published in:SIAM journal on mathematical analysis 2010-01, Vol.42 (6), p.2721-2761
Main Authors: Deng, Shengfu, Sun, Shu-Ming
Format: Article
Language:English
Subjects:
3-D technology
Approximation
Constants
Eulers equations
Infinity
Mathematical analysis
Oscillations
Studies
Three dimensional
Two dimensional
Wave propagation
Waveform analysis
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:The paper concerns three-dimensional (3D) traveling gravity-capillary waves in water of finite depth. It was well known that the waves are determined by two constants: nondimensional wave speed F (called Froude number) and nondimensional surface tension b (called Bond number). For two-dimensional (2D) waves, it was known that F = 1 is a critical value, and there were many existence results for 2D waves with large or small b. However, there was still no existence of 3D waves when F is near 1 and b is small. In this paper, the existence of 3D waves in this case is discussed. It is shown that the exact Euler equations have a generalized solitary-wave solution (solitary waves with small oscillations at infinity) which is uniformly translating in the propagation direction and periodic in the transverse direction. The first-order approximation for this 3D wave is the solution of a system of coupled Schrodinger--KdV equations. [PUBLICATION ABSTRACT]
ISSN:0036-1410
1095-7154
DOI:10.1137/09077922X