Radiation and Relaxation of Oscillons
  We study oscillons, extremely long-lived localized oscillations of a scalar
field, with three different potentials: quartic, sine-Gordon model and in a new
class of convex potentials. We use an absorbing boundary at the end of the
lattice to remove emitted radiation. The energy and the frequency of an
oscillon evolve in time and are well fitted by a constant component and a
decaying, radiative part obeying a power law as a function time. The power
spectra of the emitted radiation show several distinct frequency peaks where
oscillons release energy. In two dimensions, and with suitable initial
conditions, oscillons do not decay within the range of the simulations, which
in quartic theory reach 10^8 time units. While it is known that oscillons in
three-dimensional quartic theory and sine-Gordon model decay relatively
quickly, we observe a surprising persistence of the oscillons in the convex
potential with no sign of demise up to 10^7 time units. This leads us to
speculate that an oscillon in such a potential could actually live infinitely
long both in two and three dimensions.
