Physical aspects of the deformation of \(\mathbb {Z}_2\) kinks in a generalized \(\phi ^4\) model

Abstract

We study a generalized \(\phi ^4\) model that gives rise to BPS kink–antikink configurations with compacton-like profiles. One observes that the positive parameter controlling the generalizing function promotes an infinity degeneracy of the BPS solutions. We then use the Differential Configurational Complexity technique to distinguish the degenerate configurations, which allows us to obtain the parameter values providing the most likely field profiles. Besides, the analysis of the excitation spectrum of the model shows the existence of translational and vibrational modes. Thus, the emergence of bound states of solitons (bions) and resonance phenomena is guaranteed when analyzing the scattering of kink–antikink structures. In this way, one notes that depending on the initial velocity, the collision can be inelastic or quasi-elastic, even in the case of compacton-like configurations.