Stability of periodic peakons for the Novikov equation

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.