  We study patterns that arise in the wake of an externally triggered,
spatially propagating instability in the complex Ginzburg-Landau equation. We
model the trigger by a spatial inhomogeneity moving with constant speed. In the
comoving frame, the trivial state is unstable to the left of the trigger and
stable to the right. At the trigger location, spatio-temporally periodic
wavetrains nucleate. Our results show existence of coherent, "heteroclinic"
profiles when the speed of the trigger is slightly below the speed of a free
front in the unstable medium. Our results also give expansions for the
wavenumber of wavetrains selected by these coherent fronts. A numerical
comparison yields very good agreement with observations, even for moderate
trigger speeds. Technically, our results provide a heteroclinic bifurcation
study involving an equilibrium with an algebraically double pair of complex
eigenvalues. We use geometric desingularization and invariant foliations to
describe the unfolding. Leading order terms are determined by a condition of
oscillations in a projectivized flow, which can be found by intersecting
absolute spectra with the imaginary axis.
