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...

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Bibliographic Details
Published inMathematics in engineering Vol. 5; no. 1; pp. 1 - 14
Main Authors Sánchez, Francisco Javier Martínez, Ruiz, David
Format Journal Article
LanguageEnglish
Published AIMS Press 01.01.2023
Subjects
gross-pitaevskii equation
mountain-pass solution
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Summary: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.
ISSN:2640-3501
2640-3501
DOI:10.3934/mine.2023011