Physical aspects of the deformation of Z₂ kinks in a generalized φ⁴ model

We study in a generalized φ⁴ model the formation of BPS kink/antikink configurations with compacton-like profiles. One observes that the positive parameter controlling the generalizing function promotes an infinity degenerescence of the BPS solutions. Furthermore, the analysis of the excitation spectrum of the model shows that for values of the generalizing parameter closest to zero, there are both translational and vibrational modes. On the other hand, for sufficiently large values of the generalizing parameter, one does not observe the zero mode, and only vibrational modes emerge. 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. Finally, we apply the Differential Configurational Complexity technique to obtain the parameter values providing the most likely field profiles.