chapter  3
36 Pages

Basic methods and relevant examples

In this chapter, we give a review of several methods and approaches often used to construct exact solutions of nonlinear partial differential equations, in particular, diffusion-reaction equations. Since a general theory is missing in most cases, and its development certainly lies beyond the scope of this book, it is more instructive to revisit them by means of considering how they can be applied to particular cases rather than by giving a formal description. Also, as it fully complies with the purposes of this book, we focus on the properties of the obtained exact solutions. A question of particular interest is how the speed of the traveling fronts depends on the parameter values.