环面Gross-Pitaevskii方程行波的存在性和不存在性

IF 1.4 4区工程技术 Q3 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS Mathematics in Engineering Pub Date : 2021-10-29 DOI:10.3934/mine.2023011

F. S'anchez, D. Ruiz

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引用次数: 2

摘要

本文研究了各变量为$ T $周期的Gross-Pitaevskii方程的行波。我们证明了如果$ T $足够大，存在一个解作为相应的作用泛函的全局最小值。在亚音速情况下，我们可以使用变分方法来证明山口解的存在性。此外，我们证明了对于小$ T $，问题只允许常数解。

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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Existence and nonexistence of traveling waves for the Gross-Pitaevskii equation in tori

In this paper we consider traveling waves for the Gross-Pitaevskii equation which are $ T $-periodic in each variable. We prove that if $ T $ is large enough, there exists a solution as a global minimizer of the corresponding action functional. In the subsonic case, we can use variational methods to prove the existence of a mountain-pass solution. Moreover, we show that for small $ T $ the problem admits only constant solutions.

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