Lorentz-violating effects on topological defects generated by two real scalar fields

TL;DR

This paper investigates how Lorentz-violation affects soliton solutions in a system of two coupled scalar fields, revealing preserved stability and modified phase space behavior.

Contribution

It introduces an analytical approach to study Lorentz-violation effects on topological defects generated by coupled scalar fields, extending stability analysis.

Findings

Solutions preserve linear stability despite Lorentz violation

Lorentz violation modifies the phase space stability properties

Analytical solutions are obtained considering Lorentz violation as a small perturbation

Abstract

The influence of a Lorentz-violation on soliton solutions generated by a system of two coupled scalar fields is investigated. Lorentz violation is induced by a fixed tensor coefficient that couples the two fields. The Bogomol'nyi method is applied and first-order differential equations are obtained whose solutions minimize energy and are also solutions of the equations of motion. The analysis of the solutions in phase space shows how the stability is modified with the Lorentz violation. It is shown explicitly that the solutions preserve linear stability despite the presence of Lorentz violation. Considering Lorentz violation as a small perturbation, an analytical method is employed to yield analytical solutions.