Instability of H1$$ {H}^1 $$‐stable periodic peakons for the Novikov equation

Abstract

Periodic peaked waves of the Novikov equation have been proved to be ‐orbital stable. Utilizing the method of characteristics, we establish that the periodic peakons of the Novikov equation are linearly unstable under perturbations. Moreover, it is proved that the small initial perturbations of the above periodic peakons can lead to the blow‐up phenomenon in finite time in the nonlinear evolution of the Novikov equation.