A. Geyer and D.E. Pelinovsky

Linear and nonlinear instability of the peaked periodic wave in the reduced Ostrovsky equation


Abstract:
Stability of the peaked periodic wave in the reduced Ostrovsky equation has remained open for long time. We obtain sharp bounds on the exponential growth of the L2 norm of coperiodic perturbations to the peaked periodic wave, from which it follows that the peaked periodic wave is orbitally unstable. We also prove that the peaked periodic wave with the parabolic profile is a unique peaked wave in the space of single-lobe periodic L2 functions with zero mean.

Keywords:
Reduced Ostrovsky equation; peaked periodic waves; linear instability; nonlinear instability;