Geometric Asymptotics for Nonlinear PDE

The study of asymptotic solutions to nonlinear systems of partial differential equations is a powerful tool in the analysis of such systems and their applications in physics, mechanics, and engineering. In this book, the authors propose a method of asymptotic analysis of solutions, which can be applied in the case of the so-called smoothed shock waves, nonlinear waves which vary fast in a neighborhood of the front and slowly outside of this neighborhood. The proposed method, based on the study of geometric objects associated to the front, can be viewed as a generalization of the geometric optics (or WKB) method for linear equations.