Decay of shocklike waves into compact oscillons

Abstract

The signum-Gordon model in 1+1 dimensions possesses the exact shockwave solution with discontinuity of the field at the light cone and infinite gradient energy. The energy of a regular part of the wave inside the light cone is finite and it grows linearly with time. The initial data for such waves contain a field configuration which is null in the space and has time derivative proportional to the Dirac delta. We study regularized initial data that lead to shock-like waves with finite gradient energy. We found that such waves exist in the finite time intervals and finally they decay and produce a cascade of oscillon-like structures. A pattern of the decay is very similar to the one observed in process of scattering of compact oscillons.PACS numbers: I. INTRODUCTIONCompact oscillons [1] in the signum-Gordon model [2] are rather unusual field configurations. They do not match well any of two groups formed by (quasi-) periodic excitations of scalar fields -oscillons and breathers. Whereas the oscillons [3-8] are quasi-periodic and slowly radiating excitations observed in non-integrable field theories, the breathers [9-12] are exact and infinitely long living solutions that are present in many integrable field theories. Roughly speaking, the presence or lack of emission of the radiation from such periodic structures indicates if the model may or may not be integrable. The signum-Gordon oscillon is an exact, compact, perfectly periodic and finite energy solution. It does not radiate at all, however, when perturbed it emits some radiation [13]. Since the signum-Gordon model is a non-integrable field theory, then the existence of infinitely long living exact oscillons is a rather unusual fact. Such compact oscillons may have wider applications in theories with approximate scalling symmetry [14]. It is possible due to the fact that the signum-Gordon model emerges from many field theories with non-differentaiable potentials in the limit of small amplitude excitations [13][14][15][16]. Such more general models can support topological solitons and defects [17]. 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. This issue is a main subject of the present paper. We suspect that similar phenomena may be observed * CNPq Scholarship holder -Brazil arXiv:1909.11137v1 [hep-th]

Ein konsequenter Ansatz, um endlich konservativ erfolgreich das Gewicht zu reduzieren

“…Dies könnte Betroffenen als Ausrede dienen. Sie sollten daher mit der Realität konfrontiert werden: Das Ziel Gewichtsreduktion wird nur zu einem ganz geringen Teil durch eine Steigerung der physischen Aktivität erreicht, so wichtig und „gesund“ im Sinne einer Gefäßprävention sie auch ist 25 , 26 .…”

Compact kink and its interaction with compact oscillons

“…In fact, we observe the larger differences in the case = −0.3 around the times when the deformed kink emit radiation. It was pointed out in [16,17,38] that the radiation in non-analytic models is dominated by structures similar to oscillons of the signum-Gordon model. These structures are usually called perturbed or quasi-oscillons for distinction from the exact oscillon solutions.…”

Scattering of compact oscillons

“…One can get some analytical results considering the decay of shock waves in a cascade of oscillons. This subject has been recently studied and the results have been reported in [41].…”