Eikonal 3.1: General solution for coupled system of eikonal equations, three space dimensions

Abstract

A general solution for a coupled system of eikonal equations $u_{\mu }{u}_{\mu }=0$, $v_{\mu }{v}_{\mu }=0$, $u_{\mu }{v}_{\mu }=1$ is presented, where lower indices designate derivatives, $\mu =0,1,2,3$, and summation is implied over the repeated indices. This solution is of interest by itself due to wide applications of the eikonal equations, but the system considered also appears to be part of the reduction conditions for many equations of mathematical physics.