Ground states and droplet regimes of the extended Gross-Pitaevskii equation with Lee-Huang-Yang correction
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arXiv
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866910171804991488 |
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| author | Huang, Weijie Liu, Yang Ruan, Xinran |
| author_facet | Huang, Weijie Liu, Yang Ruan, Xinran |
| contents | We study the ground states of the extended Gross--Pitaevskii equation with the Lee--Huang--Yang correction from both theoretical and numerical perspectives. Starting from the three-dimensional model, we derive reduced one- and two-dimensional equations through nondimensionalization and dimensional reduction. We establish existence and nonexistence results for ground states in different spatial dimensions, both in free space and under confining external potentials. For the numerical computation of ground states, we propose a normalized gradient flow method with a Lagrange multiplier. The numerical results show how the model parameters affect the ground-state profiles, and reveal different regimes in the free-space parameter plane, including no-ground-state, soliton-like, and droplet-like regions. We also introduce a simple flat-top approximation for the droplet regime and present two- and three-dimensional computations to illustrate more general localized structures. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_04460 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Ground states and droplet regimes of the extended Gross-Pitaevskii equation with Lee-Huang-Yang correction Huang, Weijie Liu, Yang Ruan, Xinran Mathematical Physics 35Q55, 35P30, 65M06, 65M60 We study the ground states of the extended Gross--Pitaevskii equation with the Lee--Huang--Yang correction from both theoretical and numerical perspectives. Starting from the three-dimensional model, we derive reduced one- and two-dimensional equations through nondimensionalization and dimensional reduction. We establish existence and nonexistence results for ground states in different spatial dimensions, both in free space and under confining external potentials. For the numerical computation of ground states, we propose a normalized gradient flow method with a Lagrange multiplier. The numerical results show how the model parameters affect the ground-state profiles, and reveal different regimes in the free-space parameter plane, including no-ground-state, soliton-like, and droplet-like regions. We also introduce a simple flat-top approximation for the droplet regime and present two- and three-dimensional computations to illustrate more general localized structures. |
| title | Ground states and droplet regimes of the extended Gross-Pitaevskii equation with Lee-Huang-Yang correction |
| topic | Mathematical Physics 35Q55, 35P30, 65M06, 65M60 |
| url | https://arxiv.org/abs/2604.04460 |