Amplitude modulations and resonant decay of excited oscillons

Abstract

We show that the decay of strongly excited oscillons in a single vacuum model reveals a chaotic, fractal-like pattern very much like one found in kink-antikink collision in the $φ^4$ model. This structure can be attributed to the resonant energy transfer mechanism triggered by the modulations of amplitudes of constituent oscillons which form the excited oscillon. We also find evidence that such modulations arise as a motion of two quasi-breathers inside the constituent oscillon.

Figures (8)

• Figure 1: The potential $U(\phi)$ (black) which interpolates between two quadratic potentials: $\frac{m^2}{2}\phi^2$ (dotted) and $\frac{1}{2}\phi^2+1-m^{-2}$ (dashed). Here $m=5$.
• Figure 2: Time evolution of the value of the field at the origin $\phi(0,t)$ for different initial amplitude $A_0$. Here, $\sigma=10$.
• Figure 3: 2-bounces of two oscillons with increasing number of modulations of the amplitude. Here $A_0=0.13$, $0.134$, $0.13694$. Upper: $\phi(x,t)$. Lower $\phi(0,t).$
• Figure 4: Time $\Delta t$ between the first two bounces as a function of the number of modulations. The red line denotes the fit of the linear formula (\ref{['fit']}).
• Figure 6: An example of 3-bounce of two-oscillon solutions. Here $A_0=0.13356$.