This book offers a unique, updated insight into mathematical treatment of ray methods for nonlinear waves with applications to fluids and plasmas. It is intended to serve as a good reference book to researchers and graduate students in the considered field of mathematical physics.
The main problems of the nonlinear wave propagation treated in the book are related to shock waves, to derivations of relevant multidimensional model equations for dissipative and dispersive systems, and to wave interactions.
The text is devided into eleven chapters: Physical framework; Introductory concepts for wave motions; Ray methods for linear waves; Ray methods for nonlinear hyperbolic waves; Ray method for the propagation of discontinuities; Generalized wavefront expansion for weak shocks; Small time analysis and shock stability; Ray methods for nonlinear dispersive waves, Ray methods for nonlinear dissipative waves; Interaction of dispersive waves; Interaction of hyperbolic waves.
Each of the chapters ends by an extensive list of the most relevant references. Finally, many useful details of some lengthy derivations are given in seven appendices at the end of the book.