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

被引：307
作者：
Antoine, Xavier [1 ,2 ]
Bao, Weizhu [3 ,4 ]
Besse, Christophe [5 ,6 ]
机构：
[1] Univ Lorraine, Inst Elie Cartan Lorraine, UMR 7502, F-54506 Vandoeuvre Les Nancy, France
[2] CNRS, Inst Elie Cartan Lorraine, UMR 7502, F-54506 Vandoeuvre Les Nancy, France
[3] Natl Univ Singapore, Dept Math, Singapore 119076, Singapore
[4] Natl Univ Singapore, Ctr Computat Sci & Engn, Singapore 119076, Singapore
[5] Univ Lille Nord France, CNRS UMR 8524, Lab Paul Painleve, F-59655 Villeneuve Dascq, France
[6] Univ Lille 1 Sci & Technol, INRIA SIMPAF Team, F-59655 Villeneuve Dascq, France
来源：
COMPUTER PHYSICS COMMUNICATIONS | 2013年 / 184卷 / 12期
关键词：
Nonlinear Schrodinger equation; Gross-Pitaevskii equation; Time-splitting spectral method; Crank-Nicolson finite difference method; Absorbing boundary condition; Bose-Einstein condensation; ABSORBING BOUNDARY-CONDITIONS; SPLITTING SPECTRAL APPROXIMATIONS; FINITE-DIFFERENCE METHODS; PERFECTLY MATCHED LAYER; CENTRAL VORTEX STATES; NUMERICAL-SIMULATION; SEMICLASSICAL LIMIT; PSEUDOSPECTRAL METHOD; PRESERVING SCHEME; QUANTUM DYNAMICS;
D O I：
10.1016/j.cpc.2013.07.012
中图分类号：
TP39 [计算机的应用];
学科分类号：
081203 ; 0835 ;
摘要：
In this paper, we begin with the nonlinear Schrodinger/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. (C) 2013 Elsevier B.V. All rights reserved.
引用
收藏
页码：2621 / 2633
页数：13
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