Geometrically constrained sine-Gordon field: BPS solitons and their collisions

TL;DR

This paper develops a coupled scalar field model with a sine-Gordon sector, deriving BPS solutions with internal structures, analyzing their stability, and exploring kink-antikink collision dynamics through numerical simulations.

Contribution

It introduces a new coupled model with a geometrically constrained sine-Gordon field, deriving BPS solutions with internal structures and analyzing their stability and collision behavior.

Findings

BPS kinks with internal two-kink profiles emerge due to geometric constrictions.

Internal modes are identified that influence scattering processes.

Numerical simulations reveal distinctive collision features of the constrained kinks.

Abstract

We consider an enlarged $(1+1)$-dimensional model with two real scalar fields, $\phi$ and $\chi$ whose scalar potential $V(\phi,\chi)$ has a standard $\chi^4$ sector and a sine-Gordon one for $\phi$. These fields are coupled through a generalizing function $f(\chi)$ that appears in the scalar potential and controls the nontrivial dynamics of $\phi$. We minimize the effective energy via the implementation of the BPS technique. We then obtain the Bogomol'nyi bound for the energy and the first-order equations whose solutions saturate that bound. We solve these equations for a nontrivial $f(\chi)$. As the result, BPS kinks with internal structures emerge. They exhibit a two-kink profile. i.e. an effect due to geometrical constrictions. We consider the linear stability of these new configurations. In this sense, we study the existence of internal modes that play an important role during the scattering process. We then investigate the kink-antikink collisions, and present the numerical results for the most interesting cases. We also comment about their most relevant features.