  In this paper the non-linear wave equation with a spatial inhomogeneity is
considered. The inhomogeneity splits the unbounded spatial domain into three or
more intervals, on each of which the non-linear wave equation is homogeneous.
In such setting, there often exist multiple stationary fronts. In this paper we
present a necessary and sufficient stability criterion in terms of the length
of the middle interval(s) and the energy associated with the front in these
interval(s). To prove this criterion, it is shown that critical points of the
length function and zeros of the linearisation have the same order.
Furthermore, the Evans function is used to identify the stable branch. The
criterion is illustrated with an example which shows the existence of
bi-stability: two stable fronts, one of which is non-monotonic. The Evans
function also give a sufficient instability criterion in terms of the
derivative of the length function.
