Wavefronts and Rays as Characteristics and Asymptotics

This textbook — incorporated with many illuminating examples and exercises — is aimed at graduate students of physical sciences and engineering. The purpose is to provide a background of physics and underlying mathematics for the concept of rays, filling the gap between mathematics and physics textbooks for a coherent treatment of all topics. The authors' emphasis and extremely good presentation of the theory of characteristics, which defines the rays, accentuate the beauty and versatility of this theory. To this end, the rigour of the formulation — by a pure mathematician's standards — is downplayed to highlight the physical meaning and to make the subject accessible to a wider audience. The authors describe in detail the theory of characteristics for different types of differential equations, the applications to wave propagation in different types of media, and phenomena such as caustics.

Contents:

• Characteristic Equations of First-Order Linear Partial Differential Equations
• Characteristic Equations of Second-Order Linear Partial Differential Equations
• Characteristic Equations of First-Order Nonlinear Partial Differential Equations
• Propagation of Discontinuities for Linear Partial Differential Equations
• Caustics

Readership: Theoretical seismologists, physicists and mathematicians interested in seismology.
Key Features:

• This book is a bridge between mathematicians, mathematical physicists, and applied scientists in all fields who study wave propagation and employ ray theoretic methods
• This second, extended edition includes a new appendix/chapter on Green's functions