Some of the most important geometric integrators for both ordinary and partial differential
equations are reviewed and illustrated with examples in mechanics. The class of …

The collective behaviour of soliton ensembles (ie the solitonic gas) is studied using the
methods of the direct numerical simulation. Traditionally this problem was addressed in the …

This paper investigates the solitary wave solutions of the generalized Rosenau–Korteweg-
de Vries-regularized-long wave equation. This model is obtained by coupling the Rosenau …

A three-level linear conservative implicit finite difference scheme for solving the Rosenau–
KdV–RLW equation is proposed. The existence, uniqueness, and conservation for energy of …

In this paper, we describe a numerical method to solve numerically the weakly dispersive
fully nonlinear Serre-Green-Naghdi (SGN) celebrated model. Namely, our scheme is based …

The present book is entirely devoted to the development of mathematical models and
numerical algorithms to simulate the generation and propagation of long surface water …

In this paper, numerical solutions for the Rosenau-Korteweg-de Vries equation are studied
by using the subdomain method based on the sextic B-spline basis functions. Numerical …

We undertake a detailed comparison of the results of direct numerical simulations of the
soliton gas dynamics for the Korteweg-de Vries equation with the analytical predictions …

Soliton turbulence is studied within the framework of Gardner equation (generalized
Korteweg–de Vries equation including quadratic and cubic nonlinear terms) by virtue of the …

We study interaction of two solitons of different polarities within the framework of the
modified Korteweg–de Vries equation. Three types of soliton interaction are considered …