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We study the decay of large amplitude, almost periodic breather-like states in a deformed sine-Gordon model in one spatial dimension. We discover that these objects decay in a staggered fashion via a series of transitions, during which higher harmonics are released as short, staccato bursts of radiation. Further, we argue that this phenomenon is not restricted to one particular model, and that similar mechanisms of radiative decay of long-lived oscillating states can be observed for a wide class of physical systems, including the $phi^6$ model.
Oscillons are long-lived, slowly radiating solutions of nonlinear classical relativistic field theories. Recently it was discovered that in one spatial dimension their decay may proceed in staccato bursts. Here we perform a systematic numerical study
Oscillons are extremely long-lived, spatially-localized field configurations in real-valued scalar field theories that slowly lose energy via radiation of scalar waves. Before their eventual demise, oscillons can pass through (one or more) exceptiona
We present a new class of oscillons in the (1+1)-dimensional signum-Gordon model. The oscillons periodically move to and fro in the space. They have finite total energy, finite size, and are strictly periodic in time. The corresponding solutions of t
We use the GKZ description of periods and certain classes of relative periods on families of Barth-Nieto Calabi-Yau $(l-1)$-folds in order to solve the $l$-loop banana amplitudes with their general mass dependence. As examples we compute the mass dep
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 lin