  We analyze the nonlinear evolution of spherically symmetric wormhole
solutions coupled to a massless ghost scalar field using numerical methods. In
a previous article we have shown that static wormholes with these properties
are unstable with respect to linear perturbations. Here we show that depending
on the initial perturbation the wormholes either expand or decay to a
Schwarzschild black hole. We estimate the time scale of the expanding solutions
and the ones collapsing to a black hole and show that they are consistent in
the regime of small perturbations with those predicted from perturbation
theory. In the collapsing case, we also present a systematic study of the final
black hole horizon and discuss the possibility for a luminous signal to travel
from one universe to the other and back before the black hole forms. In the
expanding case, the wormholes seem to undergo an exponential expansion, at
least during the run time of our simulations.
