@article{Sánchez2023, 
author = {Francisco Javier Martínez Sánchez and David Ruiz},
title = {Existence and nonexistence of traveling waves for the Gross-Pitaevskii equation in tori},
year = {2023},
journal = {Mathematics in Engineering},
volume = {5},
number = {1},
pages = {1-14},
keywords = {Gross-Pitaevskii equation, mountain-pass solution},
url = {https://www.sciopen.com/article/10.3934/mine.2023011},
doi = {10.3934/mine.2023011},
abstract = {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.}
}