Stability properties of periodic traveling waves for the Intermediate Long Wave Equation

TL;DR

This paper investigates the stability of periodic traveling wave solutions with zero mean for the Intermediate Long Wave equation, extending recent mathematical methods to establish their orbital and linear stability.

Contribution

It provides new stability results for periodic waves of the Intermediate Long Wave equation using advanced analytical techniques.

Findings

Orbital stability of zero-mean periodic waves established.

Linear stability results derived for these waves.

Methodology builds on recent developments in the field.

Abstract

In this paper, we determine orbital and linear stability of periodic waves with the mean zero property related to the Intermediate Long Wave equation. Our arguments follow the recent developments in \cite{andrade-pastor}, \cite{natali} and \cite{DK} to deduce the orbital/linear stability of periodic traveling waves.