Chapter 10: Some Important Nonlinear Partial Differential Equations

Many of the equations modeling complex dynamical systems in the natural and engineering sciences are partial differential equations. For these equations the independent variables are usually the time and one or more space variables. It is important to note that a vast number of scientific and technologically interesting phenomena can be modeled in terms of a relatively small set of linear and nonlinear partial differential equations. Of further significance is the fact that several techniques exist to calculate special solutions to these equations and these particular solutions are often the ones needed to analyze the phenomena of interest.