### Abstract

We consider stability of periodic travelling waves in the generalized reduced Ostrovsky equation with respect to co-periodic perturbations. Compared to the recent literature, we give a simple argument that proves spectral stability of all smooth periodic travelling waves independent of the nonlinearity power. The argument is based on the energy convexity and does not use coordinate transformations of the reduced Ostrovsky equations to the semi-linear equations of the Klein–Gordon type.

Original language | English |
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Pages (from-to) | 1293-1314 |

Number of pages | 22 |

Journal | Letters in Mathematical Physics |

Volume | 107 |

Issue number | 7 |

DOIs | |

Publication status | Published - 2 Feb 2017 |

### Keywords

- Energy-to-period map
- Negative index theory
- Reduced Ostrovsky equations
- Stability of periodic waves

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## Cite this

Geyer, A., & Pelinovsky, D. (2017). Spectral stability of periodic waves in the generalized reduced Ostrovsky equation.

*Letters in Mathematical Physics*,*107*(7), 1293-1314. https://doi.org/10.1007/s11005-017-0941-3