Through the first five chapters of this book, the focus has been on linear partial differential equations and the methods of solutions to Laplace’s, Poisson’s, Maxwell’s, and the (homogeneous and inhomogeneous) heat and wave equations. The mathematical devices used to arrive at these solutions included Green’s functions, separation of variables, Fourier series, and Fourier transforms. It is natural ask “How do we proceed in the nonlinear case?” Nonlinear partial differential equations are inherently more difficult to solve than their linear counterparts.