Abstract
In this paper, we discuss the different splitting approaches to numerically solvethe Gross–Pitaevskii equation (GPE). The models are motivated from spinor Bose–Einsteincondensate (BEC). This system is formed of coupled mean-field equations, which are based oncoupled Gross–Pitaevskii equations. We consider conservative finite-difference schemes and spectralmethods for the spatial discretisation. Furthermore, we apply implicit or explicit time-integrators andcombine these schemes with different splitting approaches. The numerical solutions are comparedbased on the conservation of the L2-norm with the analytical solutions. The advantages of the novelsplitting methods for large time-domains are based on the asymptotic conservation of the solution ofthe soliton’s applications. Furthermore, we have the benefit of larger local time-steps and thereforeobtain faster numerical schemes.
Subject
Applied Mathematics,Computational Mathematics,General Engineering
Cited by
4 articles.
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