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...
Saved in:
Published in | Mathematics in engineering Vol. 5; no. 1; pp. 1 - 14 |
---|---|
Main Authors | , |
Format | Journal Article |
Language | English |
Published |
AIMS Press
01.01.2023
|
Subjects | |
Online Access | Get full text |
Cover
Loading…
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 |