  Non-linear effects on supernova neutrino oscillations, associated with
neutrino self-interactions, are known to induce collective flavor transitions
near the supernova core for theta_13 \neq 0. In scenarios with very shallow
electron density profiles, these transformations have been shown to couple with
ordinary matter effects, jointly producing spectral distortions both in normal
and inverted hierarchy. In this work we consider a complementary scenario,
characterized by higher electron density, as indicated by post-bounce
shock-wave simulations. In this case, early collective flavor transitions are
decoupled from later, ordinary matter effects. Moreover, such transitions
become more amenable to both numerical computations and analytical
interpretations in inverted hierarchy, while they basically vanish in normal
hierarchy. We numerically evolve the neutrino density matrix in the region
relevant for self-interaction effects. In the approximation of averaged
intersection angle between neutrino trajectories, our simulations neatly show
the collective phenomena of synchronization, bipolar oscillations, and spectral
split, recently discussed in the literature. In the more realistic (but
computationally demanding) case of non-averaged neutrino trajectories, our
simulations do not show new significant features, apart from the smearing of
``fine structures'' such as bipolar nutations. Our results seem to suggest
that, at least for non-shallow matter density profiles, averaging over neutrino
trajectories plays a minor role in the final outcome. In this case, the swap of
nu_e and nu_{\mu,\tau} spectra above a critical energy may represent an
unmistakable signature of the inverted hierarchy, especially for theta_{13}
small enough to render further matter effects irrelevant.
