Symmetry in Nonlinear Mathematical Physics - 2009

Alexey Borovskikh (Moscow State University, Russia)

Group analysis of eikonal equation for non-homogeneous and anisotropic medium

The results of the group classification of 2d and 3d eikonal equations for non-homogeneous medium (y)=1/v2(x) and eikonal equation for anisotropic medium gij(x)yiyj=1 will be presented. The main influence on the both the structure of the symmetry group and the solvability of the equation make the geometrical structure of the correspondent Rimannian space. For equations with large symmetry group explicit formulas of the solutions describing the wave front of the point source and rays are presented. The illusion of the moving source and the effect of the localization of the front are discussed.