Collective coordinates for the hybrid model

Abstract

In this work, we investigate the soliton scattering problem for anti-kink/kink and kink/anti-kink configurations. To this end, we employ two distinct methods, full simulation and collective coordinates, and compare them. We apply the collective coordinate approximation method to describe both scattering configurations in the hybrid model and show that, similar to the polynomial models [Formula: see text] and [Formula: see text], the method has limitations with respect to the initial scattering velocities. In such a way that, for certain initial velocities, the solution of collective coordinates agrees with the full simulation, and for other velocities, there is a discrepancy in the solutions obtained by these two methods. We investigate the time evolution for kink/anti-kink and anti-kink/kink scattering in the hybrid model, taking into consideration the null-vector problem. As an appendix, we performed the same inspection for kink/anti-kink scattering in the [Formula: see text] model.