Threshold dynamics of singular gravity-capillary waves.

Nonlinear dynamics of short traveling capillary-gravity waves.

We establish a Green-Nagdhi model equation for capillary-gravity waves in (2+1) dimensions. Through the derivation of an asymptotic equation governing short-wave dynamics, we show that this system possesses (1+1) traveling-wave solutions for almost all the values of the Bond number theta (the special case theta=1/3 is not studied). These waves become singular when their amplitude is larger than...

Model Equations for Gravity-capillary Waves in Deep Water

The Euler equations for water waves in any depth have been shown to have solitary wave solutions when the effect of surface tension is included. This paper proposes three quadratic model equations for these types of waves in infinite depth with a two-dimensional fluid domain. One model is derived directly from the Euler equations. Two further simpler models are proposed, both having the full gr...

Numerical simulation of capillary gravity waves excited by an obstacle in shallow water

Capillary gravity waves excited by an obstacle are investigated by numerical simulations. Under the resonant condition for which large-amplitude solitary waves are generated, solutions of the Euler equations show that the capillary effects induce the generation of short waves both upstream of the solitary waves and downstream of the obstacle. Overall characteristics of these waves agree with th...

Solitary wave Solutions of a fifth order model equation for steady capillary-gravity waves over a bump with the Bond number near 1/3

The objective of this paper is to study the existence of solitary wave solutions of a fifth order model equation for steady capillary-gravity waves over a bump with the Bond number near 1/3. We proved that there exist solitary wave solutions of the model equation for a sufficiently smooth compact bump. Key-Words: Steady capillary-gravity wave, Solitary wave solution, Compact bump.

A plethora of generalised solitary gravity-capillary water waves