Introduction

Nonlinear problems have always tantalized scientists and engineers: they fascinate, but oftentimes elude exact treatment. A great majority of nonlinear problems are described by systems of nonlinear partial differential equations (PDE) together with appropriate initial/boundary conditions; these model some physical phenomena. The nonlinear PDE systems with appropriate initial/boundary conditions can be solved effectively by means of sophisticated numerical methods and computers, with due attention to the accuracy of the solutions. The transformed system is nonlinear, but has its own invariance properties leading to new classes of exact solutions of the original system of PDEs. The activist approach to nonlinear ODEs suggests how one may build up large time approximate solutions of nonlinear PDEs by a balancing argument. The simpler PDE thus obtained is usually more amenable to analysis than the original equation. The chapter also presents an overview of the key concepts discussed in this book.