An Overview of Simple Localized Solutions of the Wave Equation

Abstract

An overview of simple localized solutions of the wave equation is presented, focused on exact solutions. We consider Bateman-type solutions, which show a Gaussian localization, localized at infinity Moses-Prosser "acoustic and electromagnetic bullets" and their time-harmonic counterparts, "X-waves", etc. Paraxial beams, including Bessel-Gauss beams, are discussed in the framework of the parabolic-equation formalism. Methods of constructing both exact and paraxial approximate solutions are described