标题： Eikonal 3.1：eikonal方程耦合系统的通解，三维空间 显示英文标题

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

摘要： 对于耦合的eikonal方程组$u_\mu u_\mu =0$, $v_\mu v_\mu =0$, $u_\mu v_\mu =1$的一般解被提出，其中下标表示导数，$\mu=0,1,2,3$，重复的指标表示求和。 该解本身由于eikonal方程的广泛应用而具有研究价值，但所考虑的系统也似乎是许多数学物理方程的约化条件的一部分。 显示英文摘要

摘要： 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.