Computational methods for the dynamics of the nonlinear Schrdinger/GrossPitaevskii equations
In this paper, we begin with the nonlinear Schrdinger/GrossPitaevskii equation (NLSE/GPE) for modeling BoseEinstein condensation (BEC) and nonlinear optics as well as other applications, and discuss their dynamical properties ranging from time reversible, time transverse invariant, mass and energy conservation, and dispersion relation to soliton solutions. Then, we review and compare different numerical methods for solving the NLSE/GPE including finite difference time domain methods and time-splitting spectral method, and discuss different absorbing boundary conditions. In addition, these numerical methods are extended to the NLSE/GPE with damping terms and/or an angular momentum rotation term as well as coupled NLSEs/GPEs. Finally, applications to simulate a quantized vortex lattice dynamics in a rotating BEC are reported.
grosspitaevskii equation boseeinstein condensation time-splitting spectral method absorbing boundary condition nonlinear schrdinger equation cranknicolson finite difference method