扎哈罗夫-库兹涅佐夫方程的有限孤波之和的渐近稳定性

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2024-08-20 DOI:10.1088/1361-6544/ad694b

Didier Pilod, Frédéric Valet

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引用次数: 0

摘要

我们证明了二维和三维扎哈罗夫-库兹涅佐夫方程有序孤波有限和的渐近稳定性。我们还推导出了轨道稳定性结果的定性版本，这将有助于在即将发表的论文中研究两个孤波的碰撞。它依赖于斜半空的单调性特性，以及 Côte、Muñoz、Pilod 和 Simpson 在二维，Farah、Holmer、Roudenko 和 Yang 在三维引入的围绕一个孤波的刚性特性。

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Asymptotic stability of a finite sum of solitary waves for the Zakharov–Kuznetsov equation

We prove the asymptotic stability of a finite sum of well-ordered solitary waves for the Zakharov–Kuznetsov equation in dimensions two and three. We also derive a qualitative version of the orbital stability result, which will be useful for studying the collision of two solitary waves in a forthcoming paper. The proof extends the ideas of Martel, Merle and Tsai for the sub-critical gKdV equation in dimension one to the higher-dimensional case. It relies on monotonicity properties on oblique half-spaces and rigidity properties around one solitary wave introduced by Côte, Muñoz, Pilod and Simpson in dimension two, and by Farah, Holmer, Roudenko and Yang in dimension three.

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来源期刊

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

期刊介绍： Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.