The wave equation in Rn is a partial differential equation, in fact the following one:
d d       d   d             d   d
---- u = ------- u + ... + ------- u
dtdt     dx1 dx1           dxn dxn
with u: Rn+1 -> R stands for the solution and initial conditions:
u(0,x) = a(x)

--- u(0,x) = b(x)
It 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 /S2
S2 is the unit sphere in R3.

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