Conserved energies for the one dimensional Gross-Pitaevskii equation

We prove the well-posedness results for the one dimensional Gross-Pitaevskii equation in the energy space, which is a complete metric space equipped with a newly introduced metric and with the energy norm describing the Hs regularities of the solutions. We establish a family of conserved energies fo...

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Bibliographic Details
Published in:Advances in mathematics (New York. 1965) 2021-01, Vol.377, p.107467, Article 107467
Main Authors: Koch, Herbert, Liao, Xian
Format: Article
Language:English
Subjects:
Conserved energies
Gross-Pitaevskii equation
Metric space
Modified Korteweg-de Vries equation
Transmission coefficient
Well-posedness
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Summary:We prove the well-posedness results for the one dimensional Gross-Pitaevskii equation in the energy space, which is a complete metric space equipped with a newly introduced metric and with the energy norm describing the Hs regularities of the solutions. We establish a family of conserved energies for the one dimensional Gross-Pitaevskii equation, such that all the energy norms of the solutions are conserved globally in time. This family of energies is also conserved by the complex modified Korteweg-de Vries flow.
ISSN:0001-8708
1090-2082
DOI:10.1016/j.aim.2020.107467