  Traveling wave solutions of reaction-diffusion equations are well-studied for
Lipschitz continuous monostable and bistable reaction functions. These special
solutions play a key role in mathematical biology and in particular in the
study of ecological invasions. However, if there are more than two stable
steady states, the invasion phenomenon may become more intricate and involve
intermediate steps, which leads one to consider not a single but a collection
of traveling waves with ordered speeds. In this paper we show that, if the
reaction function is discontinuous at the stable steady states, then such a
collection of traveling waves exists and even provides a special solution which
we call a terrace solution. More precisely, we will address both the existence
and uniqueness of the terrace solution.
