Page 1 Mathematical Surveys and Monographs Volume 188 The Water Waves Problem
Mathematical Analysis and Asymptotics David Lannes American Mathematical Society Page 2 …

Considered herein are a number of variants of the classical Boussinesq system and their
higher-order generalizations. Such equations were first derived by Boussinesq to describe …

We rigorously justify in 3 D the main asymptotic models used in coastal oceanography,
including: shallow-water equations, Boussinesq systems, Kadomtsev–Petviashvili (KP) …

Considered here are Boussinesq systems of equations of surface water wave theory over a
variable bottom. A simplified such Boussinesq system is derived and solved numerically by …

In this paper we deal with the long time existence issue for the Cauchy problem associated
to some asymptotic models for long wave, small amplitude gravity surface water waves. We …

We focus here on the water waves problem for uneven bottoms in the long-wave regime, on
an unbounded two or three-dimensional domain. In order to derive asymptotic models for …

A generalized version of the abcd-Boussinesq class of systems is derived to accommodate
variable bottom topography in two-dimensional space. This extension allows for the …

The simulation of long, nonlinear dispersive waves in bounded domains usually requires the
use of slip-wall boundary conditions. Boussinesq systems appearing in the literature are …

This paper concerns the interaction between solitary waves on the surface of an ideal fluid
and a localized external force, which models a moving disturbance on the free surface or an …

We study analytically and numerically a 2D version of a Boussinesq-type model considered
by M. Chen (2003) to describe water wave propagation on the surface of a channel with an …