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LOD-MS for Gross-Pitaevskii Equation in Bose-Einstein Condensates

Published online by Cambridge University Press:  03 June 2015

Linghua Kong ,
Jialin Hong  and
Jingjing Zhang
Linghua Kong*
Affiliation:
School of Mathematics and Information Science, Jiangxi Normal University, Nanchang, Jiangxi 330022, P.R. China
Jialin Hong*
Affiliation:
State Key Laboratory of Scientific and Engineering Computing, Institute of Computational Mathematics and Scientific/Engineering Computing, Academy of Mathematics and System Science, Chinese Academy of Sciences, P.O. Box 2719, Beijing 100190, P.R. China
Jingjing Zhang*
Affiliation:
School of Mathematics and Information Science, Henan Polytechnic University, Jiaozuo, Henan 454000, P.R. China
*
Corresponding author.Email:konglh@mail.ustc.edu.cn
Email:hjl@lsec.cc.ac.cn
Email:zhangjj@hpu.edu.cn
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Abstract

The local one-dimensional multisymplectic scheme (LOD-MS) is developed for the three-dimensional (3D) Gross-Pitaevskii (GP) equation in Bose-Einstein condensates. The idea is originated from the advantages of multisymplectic integrators and from the cheap computational cost of the local one-dimensional (LOD) method. The 3D GP equation is split into three linear LOD Schrödinger equations and an exactly solvable nonlinear Hamiltonian ODE. The three linear LOD Schrödinger equations are multisymplectic which can be approximated by multisymplectic integrator (MI). The conservative properties of the proposed scheme are investigated. It is mass-preserving. Surprisingly, the scheme preserves the discrete local energy conservation laws and global energy conservation law if the wave function is variable separable. This is impossible for conventional MIs in nonlinear Hamiltonian context. The numerical results show that the LOD-MS can simulate the original problems very well. They are consistent with the numerical analysis.

Keywords

65M0665M1265Z0570H15LOD-MSGross-Pitaevskii equationlocal one-dimensional methodmidpoint methodconservation laws
Type
Research Article
Information
Communications in Computational Physics , Volume 14 , Issue 1 , July 2013 , pp. 219 - 241
Copyright
Copyright © Global Science Press Limited 2013

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