THE PERTURBED KORTEWEG-DEVRIES EQUATION - EVOLUTION OF SOLITONS

In this paper we examine the dynamic of solitons in the presence of external forces expressed by a n-degree polynomial perturbative term or by a combination of polynomial and differential terms in the dependent variable. Under the action of these forces the soliton profile will no longer be a simple translation: asymptotic behaviour of the wave amplitude to threshold values (stationary equilibrium states) are now possible and <<explosions>> may occur at some finite <<critical time>> at which the soliton amplitude becomes infinite.