非线性Schrödinger方程中双涡行波的唯一性结果

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2023-11-11 DOI:10.2140/apde.2023.16.2173

David Chiron, Eliot Pacherie

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引用次数: 4

摘要

对于2维的非线性Schrödinger方程，Bethuel, Gravejat和Saut(2009)已经建立了固定动量下能量的全局最小值的存在性(另见Chiron和mariuz(2017)的工作)。这个最小化器是非线性Schrödinger方程的行波。对于大动量，传播速度很小，最小化器表现为两个分离良好的涡流。在这个极限下，我们证明了这个最小化器的唯一性，直到问题的不变性，从而证明了这个行波的轨道稳定性。这项工作是前两篇论文的后续，在这两篇论文中，我们构建并研究了方程的特定行波。我们在一类函数中给出了这个行波的唯一性结果，这些函数特别包含了能量的所有可能的极小值。

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A uniqueness result for the two-vortex traveling wave in the nonlinear Schrödinger equation

For the nonlinear Schrödinger equation in dimension 2, the existence of a global minimizer of the energy at fixed momentum has been established by Bethuel, Gravejat and Saut (2009) (see also work of Chiron and Mariş (2017)). This minimizer is a traveling wave for the nonlinear Schrödinger equation. For large momenta, the propagation speed is small and the minimizer behaves like two well-separated vortices. In that limit, we show the uniqueness of this minimizer, up to the invariances of the problem, hence proving the orbital stability of this traveling wave. This work is a follow up to two previous papers, where we constructed and studied a particular traveling wave of the equation. We show a uniqueness result on this traveling wave in a class of functions that contains in particular all possible minimizers of the energy.

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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.