Stability of periodic peakons for the Novikov equation

TL;DR

This paper proves that periodic peakons are globally stable weak solutions of the Novikov equation, demonstrating their shape stability under small energy space perturbations, which advances understanding of their dynamic behavior.

Contribution

It establishes the orbital stability of periodic peakons for the Novikov equation using invariants and extremum control, a novel stability result for this class of solutions.

Findings

Periodic peakons are the global weak solutions of the Novikov equation.

The shapes of periodic peakons are stable under small perturbations.

Stability proof uses invariants and extremum control techniques.

Abstract

The Novikov equation is an integrable Camassa-Holm type equation with cubic nonlinearity and admits the periodic peakons. In this paper, it is shown that the periodic peakons are the global periodic weak solutions to the Novikov equation and we also prove the orbital stability of the periodic peakons for Novikov equation. By using the invariants of the equation and controlling the extrema of the solution, it is demonstrated that the shapes of these periodic peakons are stable under small perturbations in the energy space.