# Kinks and branes in models with hyperbolic interactions

## TL;DR

This paper explores scalar field models with hyperbolic interactions, deriving analytical solutions and analyzing their stability, and extends the analysis to braneworld scenarios to construct stable, distinct models.

## Contribution

It introduces a deformation method to generate hyperbolic potentials with analytical solutions and applies both standard and non-standard formalisms to braneworld models.

## Key findings

- Analytical solutions for hyperbolic scalar field models
- Stable braneworld configurations with hyperbolic interactions
- Construction of distinct braneworld models via first order formalism

## Abstract

In this work we investigate several models described by a single real scalar field with non-polynomial interactions, constructed to support topological solutions. We do this using the deformation procedure to introduce a function which allows to construct two distinct families of hyperbolic potentials, controlled by three distinct parameters, in the standard formalism. In this way, the procedure allows us to get analytical solutions, and then investigate the energy density, linear stability and zero mode. We move on and introduce a non-standard formalism to obtain compact solutions, analytically. We also investigate these hyperbolic models in the braneworld context, considering both the standard and non-standard possibilities. The results show how to construct distinct braneworld models which are implemented via the first order formalism and are stable against fluctuation of the metric tensor.