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arXiv · 1909.11137

On decay of shock-like waves into compact oscillons

F. M. Hahne·P. Klimas·J. S. Streibel
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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.

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F. M. Hahne, P. Klimas, J. S. Streibel. 2019-09-24. On decay of shock-like waves into compact oscillons. https://doi.org/10.1103/physrevd.101.076013

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