The stability of the peaked periodic wave in the reduced Ostrovsky equation has remained an open problem for a long time. In order to solve this problem we obtain sharp bounds on the exponential growth of the L 2 norm of co-periodic perturbations to the peaked periodic wave, from which it follows that the peaked periodic wave is linearly unstable. We also prove that the peaked periodic wave with a parabolic profile is the unique peaked wave in the space of periodic L 2 functions with zero mean and a single minimum per period.
- Peaked periodic wave
- Reduced Ostrovsky equation