Collective coordinates for the hybrid model

TL;DR

This paper investigates soliton scattering in a hybrid model using collective coordinates, highlighting the method's limitations and persistent null-vector problems similar to polynomial models like 4 and 6.

Contribution

It applies the collective coordinate approximation to a hybrid model's soliton scattering, revealing its limitations and issues like null-vector problems and singularities.

Findings

The collective coordinate method agrees with full simulations at certain initial speeds.

Discrepancies occur between the method and full simulations at other initial speeds.

Null-vector problems persist in the hybrid model, similar to polynomial models.

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 $\phi^4$.