Acoustic And Electromagnetic Bullets

Abstract

We show that all finite energy, causal solutions of the time-dependent three-dimensional acoustic equation and Maxwell's equations have forms for large radius which, except for a factor 1/r represent one-dimensional wave motions along straight lines through the origin. The asymptotic region is called the wave zone.We also show, conversely, how the exact finite energy causal solutions can be obtained from the asymptotic solutions in the wave zone through the use of a refined Radon transform. We have thus obtained a way of finding exact, causal three-dimensional solutions from the essentially one-dimensional solutions in the wave zone. When the asymptotic solutions are confined to a finite radial interval within a cone, the exact solutions are termed bullets and asymptotically represent packets of acoustic and electromagnetic energy shot through the cone. No reflectors are needed. Explicit examples will be given.