Computational methods for the dynamics of the nonlinear Schrodinger/Gross-Pitaevskii equations

摘要

In this paper, we begin with the nonlinear Schrodinger/Gross-Pitaevskiiequation (NLSE/GPE) for modeling Bose-Einstein condensation (BEC) and nonlinearoptics as well as other applications, and discuss their dynamical propertiesranging from time reversible, time transverse invariant, mass and energyconservation, dispersion relation to soliton solutions. Then, we review andcompare different numerical methods for solving the NLSE/GPE including finitedifference time domain methods and time-splitting spectral method, and discussdifferent absorbing boundary conditions. In addition, these numerical methodsare extended to the NLSE/GPE with damping terms and/or an angular momentumrotation term as well as coupled NLSEs/GPEs. Finally, applications to simulatea quantized vortex lattice dynamics in a rotating BEC are reported.