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Construction of
minimizing traveling waves for the Gross–Pitaevskii equation
on $\mathbb{R} \times \mathbb{T}$
André de Laire, Philippe Gravejat and Didier Smets |
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Vol. 6 (2024), No. 1, 157–188
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Abstract |
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As a sequel to our previous analysis of the Gross–Pitaevskii equation on the product space , we construct finite energy traveling waves as minimizers of the Ginzburg–Landau energy at fixed momentum. The proof of the compactness of minimizing sequences relies on a new symmetrization argument, well-suited to the periodic setting. |
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Keywords
Gross–Pitaevskii equation, traveling waves
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Mathematical Subject Classification
Primary: 35C07, 35C08, 35J20, 35Q55, 37K40
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Milestones
Received: 11 July 2023
Accepted: 3 October 2023
Published: 20 January 2024
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Authors |
| André de Laire | |
| Laboratoire Paul Painlevé Université de Lille Cité Scientifique Villeneuve d’Ascq France |
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| Philippe Gravejat | |
| Laboratoire Analyse Géométrie
Modélisation CY Cergy Paris Université Cergy-Pontoise France |
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| Didier Smets | |
| Laboratoire Jacques-Louis
Lions Sorbonne Université Paris France |
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| © 2024 MSP (Mathematical Sciences Publishers). |
