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Title: Computational methods for the dynamics of the nonlinear Schrödinger/Gross-Pitaevskii equations
Authors: Antoine, X.
Bao, W. 
Besse, C.
Keywords: Absorbing boundary condition
Bose-Einstein condensation
Crank-Nicolson finite difference method
Gross-Pitaevskii equation
Nonlinear Schrödinger equation
Time-splitting spectral method
Issue Date: Dec-2013
Citation: Antoine, X., Bao, W., Besse, C. (2013-12). Computational methods for the dynamics of the nonlinear Schrödinger/Gross-Pitaevskii equations. Computer Physics Communications 184 (12) : 2621-2633. ScholarBank@NUS Repository.
Abstract: In this paper, we begin with the nonlinear Schrödinger/Gross- Pitaevskii equation (NLSE/GPE) for modeling Bose-Einstein 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. © 2013 Elsevier B.V. All rights reserved.
Source Title: Computer Physics Communications
ISSN: 00104655
DOI: 10.1016/j.cpc.2013.07.012
Appears in Collections:Staff Publications

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