▪ Abstract This review deals primarily with the bifurcation, stability, and evolution of gravity
and capillary-gravity waves. Recent results on the bifurcation of various types of capillary …

The main results of this paper are existence theorems for traveling gravity and capillary
gravity water waves in two dimensions, and capillary gravity water waves in three …

The main purpose of the paper is to provide a survey of our recent studies on soliton
solutions of the Kadomtsev–Petviashvili (KP) equation. The KP equation describes weakly …

An algorithm for the solution of general isotropic nonlinear wave equations is presented. The
algorithm is based on a symmetric factorization of the linear part of the wave operator …

We prove the existence of finite-energy solitary waves for isotropic Benney–Luke equations
that arise in the study of the evolution of small amplitude, three-dimensional water waves …

This paper discusses the bifurcation theory for the equations for traveling surface water
waves, based on the formulation of Zakharov [58] and of Craig and Sulem [15] in terms of …

We present an accurate and efficient numerical model for the simulation of fully nonlinear
(non-breaking), three-dimensional surface water waves on infinite or finite depth. As an …

The steady-state nearly resonant water waves with time-independent spectrum in deep
water are obtained from the full wave equations for inviscid, incompressible gravity waves in …

Spectroscopy is a fundamental tool in science which consists in studying the response of a
system as a function of frequency. Among its many applications in Physics, Biology …

We study the scattering of surface water waves with irrotational draining vortices. At small
depth, this system is a mathematical analogue of a rotating black hole and can be used to …