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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
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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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