A gradient flow model for the Gross--Pitaevskii problem: Mathematical and numerical analysis
Numerical Analysis
2025-11-03 v1 Numerical Analysis
Abstract
This paper concerns the mathematical and numerical analysis of the 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.
Keywords
Cite
@article{arxiv.2510.27235,
title = {A gradient flow model for the Gross--Pitaevskii problem: Mathematical and numerical analysis},
author = {Tianyang Chu and Xiaoying Dai and Jing Wu and Aihui Zhou},
journal= {arXiv preprint arXiv:2510.27235},
year = {2025}
}