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 highly accurate numerical scheme is presented for the Serre system of partial differential
equations, which models the propagation of dispersive shallow water waves in the fully …

We consider the periodic initial-value problem for the family of abcd Boussinesq
systems,[8],[9], and their completely symmetric analogs,[10]. We approximate their solutions …

This paper obtains the solitary wave solution of the Bona-Chen equation which is a coupled
system of nonlinear evolution equation that arises in the study of shallow water waves flow …

In this paper a family of fixed point algorithms, generalizing the Petviashvili method, is
considered. A previous work studied the convergence of the methods. Presented here is a …

We numerically study nonlinear phenomena related to the dynamics of traveling wave
solutions of the Serre equations including the stability, the persistence, the interactions and …

Some systems were recently put forth as models for studying the interaction of long and
short waves in dispersive media. These systems were shown to possess synchronized …

We provide conditions for the existence of hyperbolic, unbounded periodic and elliptic
solutions in terms of Weierstrass℘ functions of both third and fifth-order KdV–BBM (Korteweg …

We study the spectral (in) stability of one-dimensional solitary and cnoidal waves of various
Boussinesq systems. These systems model three-dimensional water waves (ie, the surface …

Singular Solutions of a Boussinesq System for Water Waves 1 Introduction Page 1 J. Math. Study
doi: 10.4208/jms.v49n3.16.01 Vol. 49, No. 3, pp. 205-220 September 2016 Singular Solutions of …