R.M. Chen and D.E. Pelinovsky
W1,∞ 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 W1,∞-perturbations. Moreover,
we show that small initial W1,∞-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.