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.

中文翻译：

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广义简化 Ostrovsky 方程中周期波的光谱稳定性

我们考虑关于共周期扰动的广义简化 Ostrovsky 方程中周期性行波的稳定性。与最近的文献相比，我们给出了一个简单的论证，证明了所有光滑周期性行波的谱稳定性与非线性功率无关。该论证基于能量凸性，并且不使用简化的 Ostrovsky 方程到 Klein-Gordon 型半线性方程的坐标变换。