Camassa–Holm, Korteweg–de Vries-5 and other asymptotically equivalent equations for shallow water waves
Abstract We derive the Camassa–Holm equation (CH) as a shallow water wave equation
with surface tension in an asymptotic expansion that extends one order beyond the …
with surface tension in an asymptotic expansion that extends one order beyond the …
On asymptotically equivalent shallow water wave equations
The integrable third-order Korteweg–de Vries (KdV) equation emerges uniquely at linear
order in the asymptotic expansion for unidirectional shallow water waves. However, at …
order in the asymptotic expansion for unidirectional shallow water waves. However, at …
[图书][B] Gravity-capillary free-surface flows
JM Vanden-Broeck - 2010 - books.google.com
Free surface problems occur in many aspects of science and of everyday life such as the
waves on a beach, bubbles rising in a glass of champagne, melting ice, pouring flows from a …
waves on a beach, bubbles rising in a glass of champagne, melting ice, pouring flows from a …
On the structure of parasitic gravity-capillary standing waves in the small surface tension limit
We present new numerical solutions for nonlinear standing water waves when the effects of
both gravity and surface tension are considered. For small values of the surface tension …
both gravity and surface tension are considered. For small values of the surface tension …
Radiationless traveling waves in saturable nonlinear Schrödinger lattices
TRO Melvin, AR Champneys, PG Kevrekidis, J Cuevas - Physical review letters, 2006 - APS
The long-standing problem of moving discrete solitary waves in nonlinear Schrödinger
lattices is revisited. The context is photorefractive crystal lattices with saturable nonlinearity …
lattices is revisited. The context is photorefractive crystal lattices with saturable nonlinearity …
Observation of depression solitary surface waves on a thin fluid layer
E Falcon, C Laroche, S Fauve - Physical review letters, 2002 - APS
We report the observation of depression solitary surface waves on a layer of mercury when
its depth is thin enough compared to the capillary length. These waves, as well as the well …
its depth is thin enough compared to the capillary length. These waves, as well as the well …
[HTML][HTML] Finite-depth effects on solitary waves in a floating ice sheet
A theoretical and numerical study of two-dimensional nonlinear flexural-gravity waves
propagating at the surface of an ideal fluid of finite depth, covered by a thin ice sheet, is …
propagating at the surface of an ideal fluid of finite depth, covered by a thin ice sheet, is …
Steady water waves
MD Groves - Journal of Nonlinear Mathematical Physics, 2004 - Springer
The classical water wave problem concerns the irrotational flow of a perfect fluid of unit
density subject to the forces of gravity and surface tension. The fluid motion is described by …
density subject to the forces of gravity and surface tension. The fluid motion is described by …
Large mode-2 internal solitary waves in three-layer flows
In this paper, we investigate mode-2 solitary waves in a three-layer stratified flow model.
Localised travelling wave solutions to both the fully nonlinear problem (Euler equations) …
Localised travelling wave solutions to both the fully nonlinear problem (Euler equations) …
The numerical computation of freely propagating time-dependent irrotational water waves
F Dias, TJ Bridges - Fluid Dynamics Research, 2006 - Elsevier
Methods for the numerical computation of freely propagating irrotational water waves are
reviewed. The emphasis is on the methods, not on the results. The primary focus is on …
reviewed. The emphasis is on the methods, not on the results. The primary focus is on …