Existence and nonexistence of traveling waves for the Gross-Pitaevskii equation in tori Martínez Sánchez, Francisco Javier Ruiz Aguilar, David Gross-Pitaevskii equation Mountain-pass solution We would like to thank the anonymous referee for their careful reading of the paper and the useful suggestions, which have improved the presentation of this work. D. R. has been supported by the FEDER-MINECO Grant PGC2018-096422-B-I00 and by J. Andalucia (FQM-116). He also acknowledges financial support from the Spanish Ministry of Science and Innovation (MICINN), through the IMAG-Maria de Maeztu Excellence Grant CEX2020-001105-M/AEI/10.13039/501100011033. 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. 2022-03-28T10:20:50Z 2022-03-28T10:20:50Z 2022-02-11 info:eu-repo/semantics/article Sánchez, F. J. M., & Ruiz, D. Existence and nonexistence of traveling waves for the Gross-Pitaevskii equation in tori. Mathematics in Engineering, 5(1): 1–14. [DOI:10.3934/mine.2023011] http://hdl.handle.net/10481/73823 10.3934/mine.2023011 eng http://creativecommons.org/licenses/by/3.0/es/ info:eu-repo/semantics/openAccess Atribución 3.0 España AIMS Press