A comment about the paper On the instability of elliptic traveling wave solutions of the modified Camassa-Holm equation

TL;DR

This paper critiques a recent study on elliptic traveling wave instability in the modified Camassa-Holm equation and establishes the orbital stability of periodic snoidal waves in the energy space.

Contribution

It corrects previous inaccuracies and proves the orbital stability of periodic snoidal waves, advancing understanding of wave stability in this context.

Findings

Corrected previous inaccuracies in the instability analysis.

Proved orbital stability of periodic snoidal waves.

Enhanced understanding of wave stability in the modified Camassa-Holm equation.

Abstract

We discuss the recent paper by A. Dar\'os and L.K. Arruda (On the instability of elliptic traveling wave solutions of the modified Camassa-Holm equation, J. Diff. Equat., 266 (2019), 1946-1968). Our intention is to correct some imperfections left by the authors and present the orbital stability of periodic snoidal waves in the energy space.