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arXiv · 1801.08386

Conserved energies for the one dimensional Gross-Pitaevskii equation

Herbert Koch·Xian Liao
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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 $H^s$ 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.

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Herbert Koch, Xian Liao. 2018-01-25. Conserved energies for the one dimensional Gross-Pitaevskii equation. https://arxiv.org/abs/1801.08386

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