Splitting methods for the Gross-Pitaevskii equation on the full space and vortex nucleation
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2026
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| _version_ | 1866914380044566528 |
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| author | Chauleur, Quentin Kemlin, Gaspard |
| author_facet | Chauleur, Quentin Kemlin, Gaspard |
| contents | We prove the convergence in Zhidkov spaces of the first-order Lie-Trotter and the second-order Strang splitting schemes for the time integration of the Gross-Pitaesvkii equation with a time-dependent potential and non-zero boundary conditions at infinity. We also show the conservation of the generalized mass and the near-preservation of the Ginzburg-Landau energy balance law. Numerical accuracy tests performed on a one-dimensional dark soliton corroborate our theoretical findings. We finally investigate the nucleation of quantum vortices in two experimentally relevant settings. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_08440 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Splitting methods for the Gross-Pitaevskii equation on the full space and vortex nucleation Chauleur, Quentin Kemlin, Gaspard Analysis of PDEs Numerical Analysis We prove the convergence in Zhidkov spaces of the first-order Lie-Trotter and the second-order Strang splitting schemes for the time integration of the Gross-Pitaesvkii equation with a time-dependent potential and non-zero boundary conditions at infinity. We also show the conservation of the generalized mass and the near-preservation of the Ginzburg-Landau energy balance law. Numerical accuracy tests performed on a one-dimensional dark soliton corroborate our theoretical findings. We finally investigate the nucleation of quantum vortices in two experimentally relevant settings. |
| title | Splitting methods for the Gross-Pitaevskii equation on the full space and vortex nucleation |
| topic | Analysis of PDEs Numerical Analysis |
| url | https://arxiv.org/abs/2603.08440 |