Computation of the radiation amplitude of oscillons

TL;DR

This paper analytically computes the radiation amplitude of small amplitude oscillons in one-dimensional scalar field theories using advanced asymptotic methods, confirming results with numerical simulations.

Contribution

It introduces an analytical approach employing matched asymptotic series and Borel summation to calculate oscillon radiation amplitude beyond all orders in perturbation theory.

Findings

Analytical radiation amplitude matches numerical simulations

Radiation amplitude is beyond all orders in perturbation theory

Method extends previous asymptotic techniques to oscillon analysis

Abstract

The radiation loss of small amplitude oscillons (very long-living, spatially localized, time dependent solutions) in one dimensional scalar field theories is computed in the small-amplitude expansion analytically using matched asymptotic series expansions and Borel summation. The amplitude of the radiation is beyond all orders in perturbation theory and the method used has been developed by Segur and Kruskal in Phys. Rev. Lett. 58, 747 (1987). Our results are in good agreement with those of long time numerical simulations of oscillons.