Scattering of compact oscillons

TL;DR

This paper investigates how generalized compact oscillons scatter in the signum-Gordon model, revealing complex interactions, jet-like cascades, and fractal-like radiation patterns despite the model's non-integrability.

Contribution

It constructs traveling oscillons using covariance and analyzes their scattering behavior, highlighting phenomena like cascade formation and shock wave emission.

Findings

Scattering transforms two incoming oscillons into two outgoing ones.

Generation of jet-like cascades during scattering.

Oscillons exhibit fractal-like radiation patterns.

Abstract

We study various aspects of the scattering of generalized compact oscillons in the signum-Gordon model in (1+1) dimensions. Using covariance of the model we construct traveling oscillons and study their interactions and the dependence of these interactions on the oscillons initial velocities and their relative phases. The scattering processes transform the two incoming oscillons into two outgoing ones and lead to the generation of extra oscillons which appear in the form of jet-like cascades. Such cascades vanish for some values of free parameters and the scattering processes, even though our model is non-integrable, resemble typical scattering processes normally observed for integrable or quase-integrable models. Occasionally, in the intermediate stage of the process, we have seen the emission of shock waves and we have noticed that, in general, outgoing oscillons have been more involved in their emission than the initial ones i.e. they have a border in form of curved world-lines. The results of our studies of the scattering of oscillons suggest that the radiation of the signum-Gordon model has a fractal-like nature.