| Abstract: |
| Stability of the peaked periodic wave in the reduced Ostrovsky equation has remained open for long time. We have obtained 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 orbitally unstable. We also prove that the peaked periodic wave with the parabolic profile is a unique weakly singular wave in the space of mean-zero periodic $L^2$ functions. |
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