Symmetric multi-field oscillons
  Oscillons are spatially localized structures that appear in scalar field
theories and exhibit extremely long life-times. We go beyond single-field
analyses and study oscillons comprised of multiple interacting fields, each
having an identical potential with quadratic, quartic and sextic terms. We
consider quartic interaction terms of either attractive or repulsive nature. In
the two-field case, we construct semi-analytical oscillon profiles for
different values of the potential parameters and coupling strength using the
two-timing small-amplitude formalism. We show that the interaction sign,
attractive or repulsive, leads to different oscillon solutions, albeit with
similar characteristics, like the emergence of "flat-top" shapes. In the case
of attractive interactions, the oscillons can reach higher values of the energy
density and smaller values of the width. For repulsive interactions we identify
a threshold for the coupling strength, above which oscillons do not exist
within the two-timing small-amplitude framework. We extend the
Vakhitov-Kolokolov (V-K) stability criterion, which has been used to study
single-field oscillons, and show that the symmetry of the potential leads to
similar equations as in the single-field case, albeit with modified terms. We
explore the basin of attraction of stable oscillon solutions numerically to
test the validity of the V-K criterion and show that, depending on the initial
perturbation size, unstable oscillons can either completely disperse or relax
to the closest stable configuration. Similarly to the V-K criterion, the decay
rate and lifetime of two-field oscillons are found to be qualitatively and
quantitatively similar to their single-field counterparts. Finally, we
generalize our analysis to multi-field oscillons and show that the governing
equations for their shape and stability can be mapped to the ones arising in
the two-field case.
