Camassa–Holm, Korteweg–de Vries-5 and other asymptotically equivalent equations for shallow water waves

HR Dullin, GA Gottwald, DD Holm - Fluid Dynamics Research, 2003 - iopscience.iop.org
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 …

On asymptotically equivalent shallow water wave equations

HR Dullin, GA Gottwald, DD Holm - Physica D: Nonlinear Phenomena, 2004 - Elsevier
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 …

[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 …

On the structure of parasitic gravity-capillary standing waves in the small surface tension limit

J Shelton, P Milewski, PH Trinh - Journal of Fluid Mechanics, 2023 - cambridge.org
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 …

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 …

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 …

[HTML][HTML] Finite-depth effects on solitary waves in a floating ice sheet

P Guyenne, EI Părău - Journal of Fluids and Structures, 2014 - Elsevier
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 …

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 …

Large mode-2 internal solitary waves in three-layer flows

A Doak, R Barros, PA Milewski - Journal of Fluid Mechanics, 2022 - cambridge.org
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) …

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 …