On the ground states of the Ostrovskyi equation and their stability
On the ground states of the Ostrovskyi equation and their stability
复制标题
奥斯特洛夫斯基方程的基态及其稳定性
DOI：
10.1111/sapm.12309
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发表时间：
2020
影响因子：
2.7
通讯作者：
Stefanov, Atanas
中科院分区：
文献类型：
--
作者：
Posukhovskyi, Iurii;Stefanov, Atanas
奥斯特洛夫斯基方程（Ostrovskyi‐Vakhnenko/short pulse）是数学物理中普遍存在的模型。它们描述了在科里奥利力作用下的水波以及光纤中“短”脉冲的振幅。在本文中，我们严格地构造地面行波这些模型的最小化的Hamilton泛函的任何fixedL 2范数。存在性论证通过补偿紧性方法进行，但它需要令人惊讶的详细傅立叶分析论证来排除最小化序列的极限的非零性。我们证明了所有这些波都是弱非退化的，并且是谱稳定的。
The Ostrovskyi (Ostrovskyi‐Vakhnenko/short pulse) equations are ubiquitous models in mathematical physics. They describe water waves under the action of a Coriolis force as well as the amplitude of a “short” pulse in an optical fiber. In this paper, we rigorously construct ground traveling waves for these models as minimizers of the Hamiltonian functional for any fixedL2norm. The existence argument proceeds via the method of compensated compactness, but it requires surprisingly detailed Fourier analysis arguments to rule out the nonvanishing of the limits of the minimizing sequences. We show that all of these waves are weakly nondegenerate and spectrally stable.
影响因子：
2.4
作者：
A. Stefanov
通讯作者：
A. Stefanov