Resonance with quasinormal modes in long-range kinks' collisions

Abstract

We consider a rational scalar field model in (1+1)-dimensions where the long-range character of the kinks is controllable. We show via numerical simulations that kinks with long-range tails on both sides can exhibit resonance windows. The resonant energy exchange mechanism occurs via the excitation of quasinormal modes, which we obtain via a spectral analysis. Additionally, we locate a resonance window in a family of $\phi^{10}$ models with long-range tails on both sides. Moreover, we propose a new algorithm for initializing long-range kink collisions, based on convection-diffusion dynamics.