Methods of separation of variables and exact solutions to nonlinear equations of mathematical physics

The book is devoted to the description and application of methods of generalized and functional separation of variables used to find exact solutions of nonlinear partial differential equations. The direct method for constructing reductions (in many respects related to the methods of functional separation of variables) and its more general version based on the principle of splitting are also considered in sufficient detail. In addition, a description of the differential constraint method is given, which generalizes many other exact methods. The presentation is accompanied by numerous examples of the use of methods for finding exact solutions of specific nonlinear equations of mathematical physics. The equations of heat and mass transfer, wave theory, hydrodynamics, nonlinear optics, combustion theory, chemical technology, biology, etc. are studied.Special attention is paid to nonlinear equations of a rather general form, which depend on one or several arbitrary functions. Such equations are the most difficult to analyze, and their exact solutions are of greater practical interest and can be used to assess the accuracy of numerical methods for solving the corresponding initial-boundary value problems. The book contains a lot of new material that has not been previously published in monographs. For a wide range of scientists, university teachers, engineers, graduate students and students specializing in applied and computational mathematics, theoretical physics, mechanics, control theory and chemical technology. Individual sections of the book and examples can be used in lecture courses on equations of mathematical physics, methods of mathematical physics and partial differential equations, for reading special courses and for conducting practical exercises