A general method is presented for the exact treatment of analytical problems that have
solutions representing solitary waves. The theoretical framework of the method is developed …

The latest results relating to the theory of nonlinear waves in dispersive and dissipative
media are reviewed. Attention is concentrated on small-amplitude solitary waves and, in …

The problem of the existence and dynamical stability of solitary wave solutions to a fifth-
order evolution equation, generalizing the well-known Korteweg-de Vries equation, is …

Boussinesq was the first to explain the existence of Scott Russell's solitary wave
mathematically. He employed a variety of asymptotically equivalent equations to describe …

We investigate linear stability of solitary waves of a Hamiltonian system. Unlike weakly
nonlinear water wave models, the physical system considered here is nonlinearly …

We consider linear instability of solitary waves of several classes of dispersive long wave
models. They include generalizations of KDV, BBM, regularized Boussinesq equations, with …

Several reduced dimension two layer models of incompressible flow are developed. These
are natural extensions of the Green-Naghdi dispersive single layer shallow water model. It is …

In this paper we study, from a numerical point of view, some aspects of stability of solitary-
wave solutions of the Bona–Smith systems of equations. These systems are a family of …

We investigate the eigenvalue problem obtained from linearizing the Green‐Naghdi
equations about solitary wave solutions. Unlike weakly nonlinear water wave models, the …

In a two-fluid system where the lower fluid is bounded below by a rigid bottom and the upper
fluid is bounded above by a free surface, two kinds of solitary waves can propagate along …