小速度下$\mathbb｛R｝^2中Gross-Pitaevskii方程中行波的矫顽力

Pub Date : 2019-11-10 DOI:10.5565/PUBLMAT6712307

D. Chiron, Eliot Pacherie

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引用次数: 6

摘要

在以前的一篇论文中，我们为二维Gross-Pitaevskii方程构造了行波的光滑分支。在这里，我们继续研究这个分支。我们给出了一些矫顽力的结果，并从中推导出线性化算子的核，一个谱稳定性的结果，以及能量空间中的唯一性结果。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Coercivity for travelling waves in the Gross-Pitaevskii equation in $\mathbb{R}^2$ for small speed

In a previous paper, we constructed a smooth branch of travelling waves for the 2 dimensional Gross-Pitaevskii equation. Here, we continue the study of this branch. We show some coercivity results, and we deduce from them the kernel of the linearized operator, a spectral stability result, as well as a uniqueness result in the energy space.

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