Scattering of compact oscillons

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 quasi-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 the form of curved worldlines.The results of our studies of the scattering of oscillons suggest that the radiation of the signum-Gordon model has a fractal-like nature.

Decay of shocklike waves into compact oscillons

“…However, this situation has changed after getting the first results of scattering of high speed oscillons, see Ref. [18]. We have found that such oscillons produce radiation that mainly consists of perturbed oscillons.…”

“…An interesting question about the oscillons is whether the oscillons may arise in the collision process of kinks, skyrmions and other topological or non-topologigal objects. Recently we have looked at the process of scattering of the signum-Gordon oscillons and emission of a radiation which, as reported in [18], is dominated by a huge number of smaller oscillons. Motivated by this study we have looked in more detail at the process of a collapse of the signum-Gordon shock waves which turns out to be an efficient process of production of oscillons.…”

“…In this paper we study solutions which are closely related with shock waves. The motivation for such a study came from the analysis of recent results for scattering of the signum-Gordon oscillons [18], where initially some shock wave-like configurations form and then they break and decay into a cascade of oscillons.…”

Semi-compactness and multiple oscillating pulses in kink scattering

“…The scattering of generalized compact oscillons in the signum-Gordon model were studied in the Ref. [73], showing the generation of oscillons in the form of jet-like cascates.…”

Topology, defects, and topological defects

“…However, the first one is characterized by a high amplitude, and its exact structure is still unknown, while the second one has a small amplitude, and its structure is well-known and has a form of a Gaussian. Originally, they were introduced in (1 + 3) dimensions [190] in the ϕ 4 model, later they were implemented for lower dimensions [191] and some other models, e.g., the signum-Gordon model [192]. Usually, oscillons are used as ansatz [70,71], however, the appearance of oscillons was observed beforehand for the sinh-deformed (1 + 1)-dimensional ϕ 4 model [74] after the procedure of a model deformation [72,73].…”