  In this paper we investigate the implementation of the so-called freezing
method for second order wave equations in one and several space dimensions. The
method converts the given PDE into a partial differential algebraic equation
which is then solved numerically. The reformulation aims at separating the
motion of a solution into a co-moving frame and a profile which varies as
little as possible. Numerical examples demonstrate the feasability of this
approach for semilinear wave equations with sufficient damping. We treat the
case of a traveling wave in one space dimension and of a rotating wave in two
space dimensions. In addition, we investigate in arbitrary space dimensions the
point spectrum and the essential spectrum of operators obtained by linearizing
about the profile, and we indicate the consequences for the nonlinear stability
of the wave.
