Nonlinear Partial Differential Equations

Abstract

So far in this text we have been mainly concerned in applying classic methods, the Adomina decomposition method [3–5], and the variational iteration method [8–10] in studying first order and second order linear partial differential equations. In this chapter, we will focus our study on the nonlinear partial differential equations. The nonlinear partial differential equations arise in a wide variety of physical problems such as fluid dynamics, plasma physics, solid mechanics and quantum field theory. Systems of nonlinear partial differential equations have been also noticed to arise in chemical and biological applications. The nonlinear wave equations and the solitons concept have introduced remarkable achievements in the field of applied sciences. The solutions obtained from nonlinear wave equations are different from the solutions of the linear wave equations [1–2].