# Twinlike Models for Kinks, Vortices and Monopoles

## TL;DR

This paper explores twinlike models supporting topological structures like kinks, vortices, and monopoles, demonstrating how different models can share solutions and energy densities while analyzing their stability properties.

## Contribution

It develops a first order framework to construct distinct models with identical solutions and energies, and examines their stability characteristics.

## Key findings

- Constructed models with identical solutions and energies
- Analyzed stability conditions for twinlike models
- Applied framework to kinks, vortices, and monopoles

## Abstract

This work deals with twinlike models that support topological structures such as kinks, vortices and monopoles. We investigate the equations of motion and develop the first order framework to show how to build distinct models with the same solution and energy density, as required to make them twinlike models. We also investigate how the stability under small fluctuations behaves and introduce the conditions to get the same stability on general grounds. In particular, we study models that support kinks, vortices and monopoles in one, two, and three spatial dimensions, respectively.