  We consider the one-dimensional KPP-equation driven by space-time white noise
and extend the construction of travelling wave solutions arising from Heavyside
initial data from [Tribe, 1996, MR1396765] to non-negative continuous functions
with compact support. As an application the existence of travelling wave
solutions is used to prove that the support of any solution is recurrent. As a
by-product, several upper measures are introduced that allow for a stochastic
domination of any solution to the SPDE at a fixed point in time.
