New results on twinlike models

TL;DR

This paper investigates twinlike scalar field models in two-dimensional spacetime, demonstrating how to construct models with identical defect structures, energy densities, and stability properties using a first-order framework.

Contribution

It introduces a method to analyze and construct twinlike models with the same defect solutions and stability characteristics within a first-order differential equation approach.

Findings

Identified conditions for twinlike models to share defect structures

Developed a first-order framework simplifying stability analysis

Constructed a family of models with identical energy densities

Abstract

In this work we study the presence of kinks in models described by a single real scalar field in bidimensional spacetime. We work within the first-order framework, and we show how to write first-order differential equations that solve the equations of motion. The first-order equations strongly simplify the study of linear stability, which is implemented on general grounds. They also lead to a direct investigation of twinlike theories, which is used to introduce a family of models that support the same defect structure, with the very same energy density and linear stability.