## Abstract

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.

Original language | English |
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Pages (from-to) | 1188-1208 |

Number of pages | 21 |

Journal | SIAM Journal on Mathematical Analysis |

Volume | 51 |

Issue number | 2 |

DOIs | |

Publication status | Published - 2019 |

## Keywords

- Characteristics
- Instability
- Peaked periodic wave
- Reduced Ostrovsky equation
- Semigroup