ABSTRACT
Chapter 4 describes the method of differential constraints. It first outlines the method for ordinary differential equations and then extends it to partial differential equations. The chapter details the application of first-, second-, and higher-order differential constraints as well as the use of several constraints. The presentation is accompanied by numerous examples of constructing exact solutions to nonlinear equations of mathematical physics. The focus is on nonlinear equations of heat and mass transfer, wave theory, and fluid dynamics, with particular attention to the most difficult equations for analysis that involve one or more arbitrary functions. The differential constraint method generalizes many other methods for constructing exact solutions to nonlinear PDEs. In its closing section, the chapter compares this method with other commonly used methods, including generalized separation of variables, functional separation of variables, the direct method of symmetry reductions, and the nonclassical method of symmetry reductions.
