| Issue |
ESAIM: M2AN
Volume 60, Number 3, May-June 2026
|
|
|---|---|---|
| Page(s) | 1297 - 1326 | |
| DOI | https://doi.org/10.1051/m2an/2026034 | |
| Published online | 01 June 2026 | |
A gradient flow model for the Gross-Pitaevskii problem: mathematical and numerical analysis
1
SKLMS, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, P.R. China
2
School of Mathematical Sciences, University of Chinese Academy of Sciences, Beijing 100049, P.R. China
* Corresponding author: This email address is being protected from spambots. You need JavaScript enabled to view it.
Received:
31
October
2025
Accepted:
7
April
2026
Abstract
This paper concerns the mathematical and numerical analysis of the L2 normalized gradient flow model for the Gross-Pitaevskii eigenvalue problem, which has been widely used to design the numerical schemes for the computation of the ground state of the Bose-Einstein condensate. We first provide the mathematical analysis for the model, including the well-posedness and the asymptotic behavior of the solution. Then we propose a normalized implicit-explicit fully discrete numerical scheme for the gradient flow model, and give some numerical analysis for the scheme, including the well-posedness and optimal convergence of the approximation. Some numerical experiments are provided to validate the theory.
Mathematics Subject Classification: 65N12 / 65N25 / 65N30
Key words: Bose-Einstein condensate / Gross-Pitaevskii problem / gradient flow / asymptotic behavior / convergence
© The authors. Published by EDP Sciences, SMAI 2026
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