R.M. Chen and D.E. Pelinovsky

W^1,∞ instability of H¹-stable peakons in the Novikov equation

Abstract:
It is known from the previous works that the peakon solutions of the Novikov equation are orbitally and asymptotically stable in H¹. We prove, via the method of char- acteristics, that these peakon solutions are unstable under W^1,∞-perturbations. Moreover, we show that small initial W^1,∞-perturbations of the Novikov peakons can lead to the finite time blow-up of the corresponding solutions.

Keywords:
Novikov equation; peakons; orbital stability and instability; finite-time blow-up.

R.M. Chen and D.E. Pelinovsky

W1,∞ instability of H1-stable peakons in the Novikov equation

W^1,∞ instability of H¹-stable peakons in the Novikov equation