Particle-inspired scheme for the Gross–Pitaevski equation: An application to Bose–Einstein condensation Original Research Article

An explicit time-staggered scheme to solve the two-dimensional Gross–Pitaevski equation in cylindrical geometry is presented. This scheme is an extension of the basic Visscherʹs algorithm to the case of a non-linear interaction and non-Cartesian geometries. Drawing upon the Hamiltonian structure of the Schroedinger equation, this scheme evolves the real and imaginary parts of the wavefunction in a way similar to trajectory integration methods used in particle simulations. The scheme is demonstrated for the study of an expanding Bose–Einstein condensate.