Group Classification of Eikonal Equations for the Wave Equation in Inhomogeneous Media

We present a group classification of the family of equations of the form (∇ψ)² = 1/v ²(x, y, z), called the eikonal equations, which are equations of characteristics for equations describing acoustic and electromagnetic waves in inhomogeneous media. For some cases of equations with linear and quadratic functions v(x, y, z), having the sense of the speed of waves in a medium, we present explicit solutions (eikonals of point sources) and completely describe the geometry of rays.__________Translated from Sovremennaya Matematika i Ee Prilozheniya (Contemporary Mathematics and Its Applications), Vol. 10, Suzdal Conference-4, 2003.