  We all know that in the dense anisotropic interior of the star,
neutrino-neutrino forward-scattering can lead to fast collective neutrino
oscillations, which has striking consequences on flavor dependent neutrino
emission and can be crucial for the evolution of a supernova and its neutrino
signal. The flavor evolution of such dense neutrino system is governed by a
large number of coupled nonlinear partial differential equations which are
almost always very difficult to solve. Although the triggering, initial linear
growth and the condition for fast oscillations to occur are understood by
"Linear stability analysis" but this fails to answer an important question:
"what is the impact of fast flavor conversion on observable neutrino fluxes or
the supernova explosion mechanism?". This is a significantly harder problem
that requires understanding the nature of the final state solution in the
nonlinear regime. Moving towards this direction we present one of the first
numerical as well as an analytical study of the coupled flavor evolution of a
non-stationary and inhomogeneous dense neutrino system in the nonlinear regime
considering one spatial dimension and a spectrum of velocity modes. This work
gives a clear picture of the final state flavor dynamics of such systems
specifying its dependence on space-time coordinates, phase space variables as
well as the lepton asymmetry and thus can have significant implications for the
supernova astrophysics as well as its associated neutrino phenomenology even
for the most realistic scenario.
