**wave equation**in

**R**

^{n}is a partial differential equation, in fact the following one:

d d d d d d ---- u = ------- u + ... + ------- u dtdt dx1 dx1 dxn dxnwith u:

**R**

^{n+1}->

**R**stands for the solution and initial conditions:

u(0,x) = a(x) d --- u(0,x) = b(x) dtIt has an unique solution for all n. (The easiest way to see that would be the Cauchy-Kovaljevskaja theorem, but it's not here yet and it is spelled wrong anyway.)

The equation describes how waves spread in an unlimited space, e.g. an infinite string.

The Huygens' Principle is connected to this equation.

And here is the solution for n=3:

1 d / / \ t / u(t,x) = --- ----| t | a(x+tu) du | + --- |b(x+tv)dv 4Pi dt \ /S2 / 4Pi /S2S2 is the unit sphere in

**R**

^{3}.