Wobbling double sine-Gordon kinks

We study the collision of a kink and an antikink in the double sine-Gordon model with and without the excited vibrational mode. In the latter case, we find that there is a limited range of the parameters where the resonance windows exist, despite the existence of a vibrational mode. Still, when the vibrational mode is initially excited, its energy can turn into translational energy after the collision. This creates one-bounce as well as a rich structure of higher-bounce resonance windows that depend on the wobbling phase being in or out of phase at the collision and the wobbling amplitude being sufficiently large. When the vibrational mode is excited, the modified structure of one-bounce windows is observed in the whole range of the model's parameters, and the resonant interval with higher-bounce windows gradually increases with the wobbling amplitude. We estimated the center of the one-bounce windows using a simple analytical approximation for the wobbling evolution. The kinks' final wobbling frequency is Lorentz contracted, which is simply derived from our equations. We also report that the maximum energy density value always has a smooth behavior in the resonance windows.

Automated summary

In this study, we investigated the collision of kink and antikink in the double sine-Gordon model with and without the excited vibrational mode. We found that the vibrational mode's initial excitation can lead to the energy converting into translational energy after the collision, resulting in a rich structure of resonance windows dependent on the wobbling phase and amplitude. The study also revealed modified structures of one-bounce windows throughout the parameter range and the increasing resonant interval with higher-bounce windows as the wobbling amplitude grows. The final wobbling frequency of the kinks was Lorentz contracted, and the maximum energy density value behaved smoothly in the resonance windows.