This paper, which is largely the fruit of an invited talk on the topic at the latest International
Conference on Coastal Engineering, describes the state of the art of modelling by means of …

The stability of nonlinear waves has a distinguished history and an abundance of richly
structured yet accessible examples, which makes it not only an important subject but also an …

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 continue a recently developed systematic approach to the Bousinesq (Bsq) hierarchy
and its algebro-geometric solutions. Our formalism includes a recursive construction of Lax …

Transitions are to be found throughout the natural world. The laws of nature are usually
represented by differential equations, which can be regarded as dynamical systems—both …

This book provides a self-contained presentation of classical and new methods for studying
wave phenomena that are related to the existence and stability of solitary and periodic …

A class of fully discrete schemes for the numerical simulation of solutions of the periodic
initial-value problem for a class of generalized Korteweg-de Vries equations is analysed …

The Boussinesq equation can describe wave motions in media with damping mechanism,
eg, the propagation of long waves in shallow water and the oscillations of nonlinear elastic …

We consider the stability of multi‐or n‐soliton solutions to the Korteweg‐de Vries equation
(KdV) posed on the real line. It is shown that in the standard variational characterization of …

Analytical solutions and physical interpretations for the shallow water wave system, which is
the modeling of a physical phenomenon in applied mathematics, are presented in this study …