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Fine Structure of Oscillons in the Spherically Symmetric $ϕ^4$ Klein-Gordon Model

Ethan P. Honda·Matthew W. Choptuik
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Abstract

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 non-existent or higher than previously believed. Our results are generated using a novel technique for implementing non-reflecting boundary conditions in the finite difference solution of wave equations. The method uses a coordinate transformation which blue-shifts 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.

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Ethan P. Honda, Matthew W. Choptuik. 2001-10-08. Fine Structure of Oscillons in the Spherically Symmetric $ϕ^4$ Klein-Gordon Model. https://doi.org/10.1103/physrevd.65.084037

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