A High-Order Conservative Numerical Method for Gross–Pitaevskii Equation with Time-Varying Coefficients in Modeling BEC**Supported by the National Natural Science Foundation of China under Grant Nos 11571366 and 11501570, the Open Foundation of State Key Laboratory of High Performance Computing of China, the Research Fund of National University of Defense Technology under Grant No JC15-02-02, and the Fund from HPCL.

Abstract

We propose a high-order conservative method for the nonlinear Schrödinger/Gross–Pitaevskii equation with time-varying coefficients in modeling Bose–Einstein condensation (BEC). This scheme combined with the sixth-order compact finite difference method and the fourth-order average vector field method, finely describes the condensate wave function and physical characteristics in some small potential wells. Numerical experiments are presented to demonstrate that our numerical scheme is efficient by the comparison with the Fourier pseudo-spectral method. Moreover, it preserves several conservation laws well and even exactly under some specific conditions.