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

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.

Source: arXiv:2603.08440v1 - http://arxiv.org/abs/2603.08440v1 PDF: https://arxiv.org/pdf/2603.08440v1 Original Link: http://arxiv.org/abs/2603.08440v1