Defect structures in sine-Gordon-like models

TL;DR

This paper explores various sine-Gordon-like models with real scalar fields, identifying stable topological defect solutions, including BPS states, and analyzing how these solutions bifurcate among multiple sectors.

Contribution

It introduces methods to find BPS solutions in single and two-field sine-Gordon models, including deformations and bifurcation analysis of topological sectors.

Findings

Stable defect solutions are found in multiple models.

BPS solutions are obtained via deformation and integrating factors.

Bifurcation among topological sectors is characterized.

Abstract

We investigate several models described by real scalar fields, searching for topological defects. Some models are described by a single field, and support one or two topological sectors, and others are two-field models, which support several topological sectors. Almost all the defect structures that we find are stable and finite energy solutions of first-order differential equations that solve the corresponding equations of motion. In particular, for the double sine-Gordon model we show how to find small and large BPS solutions as deformations of the BPS solution of the $\phi^4$ model. And also, for most of the two field models we find the corresponding integrating factors, which lead to the complete set of BPS solutions, nicely unveiling how they bifurcate among the several topological sectors.