A generalized-Laguerre–Hermite pseudospectral method for computing symmetric and central vortex states in Bose–Einstein condensates

A generalized-Laguerre–Hermite pseudospectral method is proposed for computing symmetric and central vortex states in Bose–Einstein condensates (BECs) in three dimensions with cylindrical symmetry. The new method is based on the properly scaled generalized-Laguerre–Hermite functions and a normalized gradient flow. It enjoys three important advantages: (i) it reduces a three-dimensional (3D) problem with cylindrical symmetry into an effective two-dimensional (2D) problem; (ii) it solves the problem in the whole space instead of in a truncated artificial computational domain and (iii) it is spectrally accurate. Extensive numerical results for computing symmetric and central vortex states in BECs are presented for one-dimensional (1D) BEC, 2D BEC with radial symmetry and 3D BEC with cylindrical symmetry.