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On decay of shock-like waves into compact oscillons
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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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Scattering of compact oscillons
Colliding exact compact oscillons in the signum-Gordon model produce outgoing quasi-oscillons and oscillon cascades, with fine-tuned phases yielding almost radiation-free scattering and a self-similar cascade hinting ...
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