Collective coordinates for the hybrid model

Abstract: In the present work, we carry out the study of scattering solitons for the anti-kink/kink and kink/anti-kink configurations. Furthermore, we can observe the same effects as those described by D. Bazeia et al.. We apply the collective coordinate approximation method to describe both scattering configurations and verify that just as happens in the polynomial models $\phi^4$ and $\phi^6$, the method has its limitations regarding the initial scattering speeds. In such a way that, for certain initial speeds, the solution of collective coordinates agrees with the fullsimulation, and for other speeds, there is a discrepancy in the solutions obtained by these two methods. We also noticed that, considering the hybrid model, the null-vector problem persists for both configurations, and when trying to fix it, a singularity is created in moduli-space as well as in $\phi^4$.