If $u(x, t)$ satisfies the wave equation $u_{t t}=u_{x x}$ , then \begin{align} u(x+h, t+k)+u(x-h, t-k)=u(x+k, t+h)+u(x-k, t-h)\end{align} for all $x, t, h,$ and $k .$
This is an exercise (exercise 4,pp41) in the Strauss's monograph Partial Differential Equations.
What is the meaning of this identity?