Nonlinear PDE Models: Soliton Solutions

Abstract

Nonlinear PDEs display a rich spectrum of solutions which in most cases must be obtained by numerical means. Some illustrations of applying explicit numerical schemes to linear and nonlinear PDEs will be given in Chapter 14. There exist special analytic solutions to some nonhnear PDEs of physical interest, the most well-known being so-called soliton solutions of nonlinear wave equations, the subject of this chapter. A soliton is a stable solitary wave or pulse. A solitary wave is a localized pulse solution which can propagate at some characteristic velocity without changing shape despite the “tug of war” between competing terms in the governing equation of motion.