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

TL;DR

This paper investigates the physical properties and dynamics of $bZ_2$ kinks in a generalized $bphi^4$ model, revealing degeneracy, excitation spectra, and scattering behaviors of soliton configurations.

Contribution

It introduces a generalized $bphi^4$ model with compacton-like BPS solutions, analyzes degeneracy and excitation spectra, and explores collision dynamics of kinks and antikinks.

Findings

Degeneracy of BPS solutions increases with a parameter.

Existence of translational and vibrational modes in the spectrum.

Collision outcomes vary between inelastic and quasi-elastic depending on initial velocity.

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 degenerescence 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.