Pulse Propagation in Inhomogeneous Media

Abstract

Approximate solutions are developed for one-dimensional pulse propagation in a medium with an analytic wave speed when the ratio ε of the pulse length to a characteristic length of the wave speed variation is small. The solutions describe an 0(1) transmitted pulse, given by the WKB solution, and an 0(ε) reflection which may progress in the opposite direction. Two approximations for the reflection are given, one in terms of explicit integrals and the other, which may be uniformly valid, by a combination of explicit integrals and a slowly varying numerical term. Comparisons with the exact solution in several examples show the usefulness of the approximate solutions.