# Periodic Traveling-wave solutions for regularized dispersive equations: Sufficient conditions for orbital stability with applications

## TL;DR

This paper introduces a new criterion for the orbital stability of periodic waves in regularized dispersive equations, applicable to fifth-order models and based on minimization of a functional, without requiring Hessian positivity.

## Contribution

It provides a novel stability criterion that does not depend on Hessian positivity and applies it to establish stability in fifth-order dispersive models.

## Key findings

- Established a new stability criterion for periodic waves.
- Proved orbital stability for a fifth-order dispersive model.
- Demonstrated stability via functional minimization.

## Abstract

In this paper, we establish a new criterion for the orbital stability of periodic waves related to a general class of regularized dispersive equations. More specifically, we present sufficient conditions for the stability without knowing the positiveness of the associated hessian matrix. As application of our method, we show the orbital stability for the fifth-order model. The orbital stability of periodic waves resulting from a minimization of a convenient functional is also proved.