# Conserved energies for the one dimensional Gross-Pitaevskii equation

Koch, H.; Liao, Xian

##### Abstract:
We prove the global-in-time well-posedness of 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 H$^{8}$ regularities of the solutions. We establish a family of conserved energies for the one dimensional Gross-Pitaevskii equation, such that 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.

 Zugehörige Institution(en) am KIT Institut für Analysis (IANA) Publikationstyp Forschungsbericht/Preprint Publikationsjahr 2020 Sprache Englisch Identifikator KITopen-ID: 1000126166 Vorab online veröffentlicht am 26.10.2020 Nachgewiesen in arXiv Relationen in KITopen Verweist aufConserved energies for the one dimensional Gross-Pitaevskii equation [in press]. Koch, H.; Liao, Xian (2020) Zeitschriftenaufsatz (1000126036)
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