In this paper, the numerical solutions are proposed for the 1D Benjamin–Bona–Mahony
(BBM) equation and 2D coupled BBM system by using Galerkin finite element technique. In …

A nonlinear dispersive model equation is used to study the onset of breaking in long waves
behind the front of an undular bore. According to experiments conducted by Favre (1935)[1] …

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 …

We review here the derivation of many of the most important models that appear in the
literature (mainly in coastal oceanography) for the description of waves in shallow water. We …

Depth-integrated long-wave models, such as the shallow-water and Boussinesq equations,
are standard fare in the study of small amplitude surface waves in shallow water. While the …

This paper is devoted to the theoretical and numerical investigation of the initial boundary
value problem for a system of equations used for the description of waves in coastal areas …

The present study is devoted to the problem of tsunami wave generation. The main goal of
this work is twofold. First of all, we propose a simple and computationally inexpensive model …

We investigate the potential and limitations of the wave generation by disturbances moving
at the bottom. More precisely, we assume that the wavemaker is composed of an underwater …

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 …

We consider a class of Boussinesq systems of Bona-Smith type in two space dimensions
approximating surface wave flows modelled by the three-dimensional Euler equations. We …