Taylor and Francis Anile, M: Ray Methods for Nonlinear Waves in Fluids and Plas

Chapter 3 recalls the basic ray methods for linear wave propagation. The fourth chapter treats the ray methods for hyperbolic waves and discusses some applications, while the fifth chapter studies the propagation of weak discontinuities and characteristic shocks. In chapter 6 the authors present an appropriate extension of the ray method, called Generalized Wavefront Expansion in order to treat the propagation of weak shocks. Chapter 7 is esentially devoted to shock stability analysis using ray methods. Chapters 8 and 9 present the systematic development of the perturbation reduction method in several dimensions for nonlinear dispersive and dissipative systems. Several applications are given to fluids and plasmas. Various model equations are obtained in several dimensions (Burgers, nonlinear Schrodinger, Kadometsey-Petviashvili). Physical interpretation of the results are also discussed. In chapter 10 the theory of dispersive wave interaction is treated in detail. Chapter 11 is entirely devoted to the interaction of hyperbolic waves. Several applications to gasdynamics and elasticity are discussed in depth.