# Stability of kinklike structures in generalized models

## TL;DR

This paper investigates the stability of kink-like topological structures in generalized scalar field models, focusing on the mathematical conditions for stability, supersymmetric factorization, and shape invariance to analyze eigenstates.

## Contribution

It introduces a framework for analyzing stability via Sturm-Liouville equations and explores supersymmetric operators and shape invariance in the context of scalar field models.

## Key findings

- Stability is governed by a Sturm-Liouville equation.
- Explicit supersymmetric operators can be constructed for stability analysis.
- Shape invariance aids in calculating discrete eigenstates.

## Abstract

We study the stability of topological structures in generalized models with a single real scalar field. We show that it is driven by a Sturm-Liouville equation and investigate the conditions that lead to the existence of explicit supersymmetric operators that factorize the stability equation and allow us to construct partner potentials. In this context, we discuss the property of shape invariance as a possible manner to calculate the discrete states and their respective eigenvalues.