It has been recently shown that the flavor composition of a self-interacting
neutrino gas can spontaneously acquire a time-dependent pulsating component
during its flavor evolution. In this work, we perform a more detailed study of
this effect in a model where neutrinos are assumed to be emitted in a
two-dimensional plane from an infinite line that acts as a neutrino antenna. We
consider several examples with varying matter and neutrino densities and find
that temporal instabilities with various frequencies are excited in a cascade.
We compare the numerical calculations of the flavor evolution with the
predictions of linearized stability analysis of the equations of motion. The
results obtained with these two approaches are in good agreement in the linear
regime, while a dramatic speed-up of the flavor conversions occurs in the
non-linear regime due to the interactions among the different pulsating modes.
We show that large flavor conversions can take place if some of the temporal
modes are unstable for long enough, and that this can happen even if the matter
and neutrino densities are changing, as long as they vary slowly.Comment: v2: revised version, 15 pages, 6 figures. Minor changes. Typos
removed, figures improved. Matches the version accepted on JCA
