A gradient flow model for the Gross-Pitaevskii problem: mathematical and numerical analysis
Abstract
This paper concerns the mathematical and numerical analysis of the L 2 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.
Fields of Study & Subjects
Cold Atom Physics and Bose-Einstein Condensates
Advanced Mathematical Physics Problems
Numerical methods for differential equations
Publication details
- Journal / source
- ESAIM Mathematical Modelling and Numerical Analysis
- Volume
- 60
- Issue
- 3
- Pages
- 1297–1326
- Publication date
- 17 April 2026
- Language
- EN