ABSTRACT
This chapter provides some of the features with the help of some interesting model equations. It discusses the analysis of these equations only to a limited extent, the main purpose being elucidation of the exact linearisation process. The chapter explores the transforming nonlinear partial differential equations (PDE) to linear PDEs exactly, some comments on the solution. It also discusses the present example for two reasons: first to show how even complicated nonlinear flows with free surfaces may have exact solutions, and second to demonstrate that while the original PDE system may not be linearisable, its changed ODE form in terms of similarity variable may admit exact linearisation. The sound speed square cs2 is kept free and is exploited to maximize symmetries and, hence, reduction of PDEs to ODEs via a similarity transformation. The transformation is clearly a generalisation of the Cole-Hopf transformation and generates a large class of nonlinear PDEs whose potential must be carefully examined.
