Consider the equation $$\frac{d^2u}{dt^2}=c^2\frac{d^2u}{dx^2}$$ where c is some constant. Define new variables, $\sigma=x-ct $ and $\gamma=x+ct$. Now show that the equation becomes $$\frac{d^2u}{d\gamma d\sigma}$$
Can somebody explain what is happening here. I do not know what $u$ is nor what it is a function of. Would this have anything to deal with the wave equation in Physics?
This question is the same as to $\frac{\partial^2 u}{\partial t^2}-c^2\frac{\partial^2u}{\partial x^2}=0\text{ implies } \frac{\partial^2 u}{\partial z \partial y}=0$