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arXiv · 2603.08440

Splitting methods for the Gross-Pitaevskii equation on the full space and vortex nucleation

Quentin Chauleur·Gaspard Kemlin
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Abstract

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.

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Quentin Chauleur, Gaspard Kemlin. 2026-03-09. Splitting methods for the Gross-Pitaevskii equation on the full space and vortex nucleation. https://arxiv.org/abs/2603.08440

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