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 $$\phi ^{10}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msup> <mml:mi>ϕ</mml:mi> <mml:mn>10</mml:mn> </mml:msup> </mml:math> 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.