ABSTRACT
Chapter 2 describes the methods of functional separation of variables that allow one to construct efficiently exact solutions to many nonlinear PDEs. It begins with a simplified method for constructing functional separable solutions and discusses solutions of a special form. The chapter then considers the differentiation method used to obtain a standard bilinear functional equation, further solved with the splitting method. Direct methods for constructing functional separable solutions in explicit or implicit form are described. The focus is on nonlinear equations of heat and mass transfer and wave theory, with particular attention to the most challenging equations for analysis that involve one or more arbitrary functions. The application of the methods is illustrated with numerous examples and tables. The general functional separations of variables and generalized splitting principle are outlined. The chapter deals with various nonlinear PDEs, including those with variable coefficients, of arbitrary order, and in two or more independent variables.
