Simplest oscillon and its sphaleron

Abstract

Oscillons in a simple, one-dimensional scalar field theory with a cubic potential are discussed. The theory has a classical sphaleron, whose decay generates a version of the oscillon. A good approximation to the small-amplitude oscillon is constructed explicitly using the asymptotic expansion of Fodor et al., but for larger amplitudes a better approximation uses the discrete, unstable, and stable deformation modes of the sphaleron.