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

TL;DR

This paper presents a general solution for a coupled system of eikonal equations in three space dimensions, which has broad applications in physics and mathematical modeling.

Contribution

It introduces a novel general solution for a specific coupled eikonal system, expanding the analytical tools available for such equations.

Findings

Provides a closed-form general solution for the coupled system

Highlights the relevance of the system in physics and mathematical reductions

Enhances understanding of eikonal equations in multiple 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.