๐”– Bobbio Scriptorium
โœฆ   LIBER   โœฆ

The long-wave limit for the water wave problem I. The case of zero surface tension

โœ Scribed by Guido Schneider; C. Eugene Wayne

Publisher
John Wiley and Sons
Year
2000
Tongue
English
Weight
375 KB
Volume
53
Category
Article
ISSN
0010-3640

No coin nor oath required. For personal study only.

โœฆ Synopsis

The Korteweg-de Vries equation, Boussinesq equation, and many other equations can be formally derived as approximate equations for the two-dimensional water wave problem in the limit of long waves. Here we consider the classical problem concerning the validity of these equations for the water wave problem in an infinitely long canal without surface tension. We prove that the solutions of the water wave problem in the long-wave limit split up into two wave packets, one moving to the right and one to the left, where each of these wave packets evolves independently as a solution of a Korteweg-de Vries equation. Our result allows us to describe the nonlinear interaction of solitary waves.

๐Ÿ“œ SIMILAR VOLUMES

The zero surface tension limit two-dimen
The zero surface tension limit two-dimensional water waves
โœ D. Ambrose; N. Masmoudi ๐Ÿ“‚ Article ๐Ÿ“… 2005 ๐Ÿ› John Wiley and Sons ๐ŸŒ English โš– 212 KB ๐Ÿ‘ 1 views

## Abstract We consider twoโ€dimensional water waves of infinite depth, periodic in the horizontal direction. It has been proven by Wu (in the slightly different nonperiodic setting) that solutions to this initial value problem exist in the absence of surface tension. Recently Ambrose has proven tha

An Apparatus for the Study of Surface Lo
An Apparatus for the Study of Surface Longitudinal Waves at the Air/Water Interface
โœ Qiang Jiang; Y.C. Chiew; J.E. Valentini ๐Ÿ“‚ Article ๐Ÿ“… 1993 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 186 KB

An apparatus used to study air/water interfacial surface viscoelasticity through longitudinal waves is described. The longitudinal surface waves are generated by an oscillating barrier driven by a small DC motor and detected with a capillary wave. The damping coefficient and the wavenumber of the lo

About embedded eigenvalues for a spectra
About embedded eigenvalues for a spectral problem arising in the study of elastic surface waves in a topographical waveguide
โœ Mourad Sini ๐Ÿ“‚ Article ๐Ÿ“… 2002 ๐Ÿ› John Wiley and Sons ๐ŸŒ English โš– 161 KB ๐Ÿ‘ 1 views

## Abstract In this paper, we are interested with the spectral study of an operator given by an elastic topographical waveguide, a deformed halfโ€space, of which the crossโ€section is a local perturbation of a homogeneous halfโ€plane. We look for guided waves propagating more rapidly than Rayleigh wav