A two-parameter continuation algorithm using radial basis function collocation method for rotating Bose–Einstein condensates

Abstract

We present an efficient numerical algorithm to observe the dynamical formation of vortex lattice of a rotating trapped Bose–Einstein condensate (BEC) via solving a two-dimensional Gross–Pitaevskii equation (GPE). We use a radial basis function collocation method (RBFCM) to discretize a two-dimensional coupled nonlinear Schrödinger equation (CNLSE) derived from the GPE. A two-parameter continuation algorithm is implemented here to trace the solution curve of the CNLSE. The numerical experiments show promise of the proposed method to observe a variety of vortices of a rotating BEC in optical lattices, and depict the densities of superfluid and the solution curves as a function of chemical potential and the rotation frequency for various vortex structures. This algorithm provides an efficient method for observing complicated convex structures and dynamical phenomena of vortices in rotating BEC when comparing with those existing numerical methods in the literature.