Numerical study of some aspects of solitary wave

Abstract

The phenomenon of the solitary wave, which was discovered by the famous British scientist Scott Russell as early as in 1834, has been greatly concerned with the development of the physics and mathematics. Now it has been proved that a large number of nonlinear evolution equations have the soliton solution by the numerical calculations and the theoretical analysis. Solitary waves have the striking property of particles. So Kruskal and Zabusky named them solitons . The solitary waves not only have been observed in nature, some of them have also been produces in laboratories now. Also, when two or three of the solitary waves interact it appears that solitary waves retains shape after interaction, despite the fact that some studies show the appearance of small tail after the collision as shown latter in the thesis. However, these properties lead scientist to do more research work in this area during the past decades through both numerical and analytical solutions of their equations. In fact, finding the analytical solutions of the nonlinear evolutionary equations generally is difficult and probably impossible in some cases; as in the case of interaction of two and three solitary waves or in case of development of Maxwellian initial condition into solitary waves. So finding the accurate approximate solution for these equations is the main aim of the researchers in order to study solitary waves on a wide range and to investigate their properties. The nonlinear waves in shallow water are of great interest of many researchers. Its importance comes from its capability for describing many physical phenomena in the fields of physics, mathematics and engineering. These nonlinear waves were mathematically modeled by the Korteweg-de Vries. The derived equation is well known Korteweg-de Vries (KdV) equation. Such a powerful equation could successfully simulate the red spots at Jupiter. Moreover, the giant ocean waves knownas Tsunami are also described by the KdV equation.