Fine structure of oscillons in the spherically symmetricφ4Klein-Gordon model

We present results from a study of the fine structure of oscillon dynamics in the $3+1$ spherically symmetric Klein-Gordon model with a symmetric double-well potential. We show that in addition to the previously understood longevity of oscillons, there exists a resonant (and critical) behavior which exhibits a time-scaling law. The mode structure of the critical solutions is examined, and we also show that the upper bound to oscillon formation (in $r_0$ space) is either nonexistent or higher than previously believed. Our results are generated using a novel technique for implementing nonreflecting boundary conditions in the finite difference solution of wave equations. The method uses a coordinate transformation which blueshifts and “freezes” outgoing radiation. The frozen radiation is then annihilated via dissipation explicitly added to the finite-difference scheme, with very little reflection into the interior of the computational domain.