Multi-kinks and composite oscillons in a commensurable and non degenerate double sine-Gordon model

In this paper, we introduce a commensurable and non-degenerate double sine-Gordon model, in which a partial breaking of vacuum degeneracy provides a mechanism for the emergence of static multi-kinks. These multi-kinks $K_n$ are stable field configurations with internal structure, consisting of $n$ localized energy packets with well-defined separations. The properties of the multi-kinks are thoroughly analyzed, including the novel phenomenology that arises during their collisions. In particular, we observe the emergence of long-lived composite oscillons that reflect the original structure of the multi-kinks. The sub-kink’s positions and their vibration modes provide collective coordinates that are used to construct a phenomenological model, which offers a good qualitative explanation of the observed oscillon properties. Radiation effects are consistently incorporated, revealing that they play an important role in the observed synchronization of the oscillon’s vibrational components.