Waves and Hyperbolic Equations
Waves are everywhere, literally, and our senses are acutely attuned to waves of various types: mechanical, water, acoustic, electromagnetic, optical, etc. Moreover, quantum mechanics tells us that matter itself is, in a sense, indistinguishable from waves. In this chapter we concentrate on properties of linear waves in dispersive media; a discussion of nonlinear waves will be postponed until Chaps. 12–14. Here the methods of choice are integral transforms and asymptotic relations, especially the Fourier transform and the stationary phase method.