Conserved energies for the one dimensional Gross-Pitaevskii equation: Low regularity case

We construct a family of conserved energies for the one dimensional Gross-Pitaevskii equation, but in the low regularity case (in [14] we have constructed conserved energies in the high regularity situation). This can be done thanks to regularization procedures and a study of the topological structu...

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Bibliographic Details
Published in:Advances in mathematics (New York. 1965) 2023-05, Vol.420, p.108996, Article 108996
Main Authors: Koch, Herbert, Liao, Xian
Format: Article
Language:English
Subjects:
Asymptotic phase change
Conserved energies
Gross-Pitaevskii equation
Regularization
Renormalized momentum
Transmission coefficient
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Summary:We construct a family of conserved energies for the one dimensional Gross-Pitaevskii equation, but in the low regularity case (in [14] we have constructed conserved energies in the high regularity situation). This can be done thanks to regularization procedures and a study of the topological structure of the finite-energy space. The asymptotic (conserved) phase change on the real line with values in R/2πZ is studied. We also construct a conserved quantity, the renormalized momentum H1 (see Theorem 1.3), on the universal covering space of the finite-energy space.
ISSN:0001-8708
1090-2082
DOI:10.1016/j.aim.2023.108996