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Research Article | Open Access

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

Francisco Javier Martínez Sánchez1, David Ruiz2
Universidad de Jaén, Departamento de Matemáticas, Campus Las Lagunillas, 23071 Jaén, Spain
IMAG, Universidad de Granada, Departamento de Análisis Matemático, 18071 Granada, Spain
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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.

Keywords

Gross-Pitaevskii equationmountain-pass solution

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Mathematics in Engineering
Volume 5 Issue 1,
February 2023
Pages 1-14
DOI: 10.3934/mine.2023011

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Sánchez FJM, Ruiz D. Existence and nonexistence of traveling waves for the Gross-Pitaevskii equation in tori. Mathematics in Engineering, 2023, 5(1): 1-14. https://doi.org/10.3934/mine.2023011

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Received: 02 November 2021
Revised: 07 January 2022
Accepted: 10 January 2022
Published: 15 February 2023
©2023 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)