A mass conserved splitting method for the nonlinear Schr?dinger equation

doi:10.1186/1687-1847-2012-85

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	A mass conserved splitting method for the nonlinear Schr?dinger equation
	Hua,Dong-Ying 1; Li,Xiang-Gui 1; Zhu,Jiang 2
	2012-06-21
发表期刊	Advances in Difference Equations
ISSN	1687-1847
卷号	2012 期号:1
摘要	AbstractA mass conserved time-splitting difference method is presented for the one-dimensional dipolar Bose-Einstein condensates (BECs) described by a nonlocal nonlinear Schr?dinger equation with a convolution term. As a result of the singularity in the convolution term, it brings difficulties both in mathematical analysis and in numerical simulations. By properly using the difference scheme to deal with the convolution term, an imaginary time method is given to compute the ground states and then a time-splitting method is obtained for dynamics of dipolar BECs. This time-splitting numerical method is mass conserved everywhere, and it has second-order accuracy and is also unconditionally stable. Numerical results are given to verify the stability and energy conservation when there is no blow up.Mathematics Subject Classification (2010) 65M06; 35Q41.
关键词	time-splitting finite difference dipolar Bose-Einstein condensates Schr?dinger equation conservation
DOI	10.1186/1687-1847-2012-85
语种	英语
WOS记录号	BMC:10.1186/1687-1847-2012-85
出版者	Springer International Publishing
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/315
专题	中国科学院数学与系统科学研究院
通讯作者	Li,Xiang-Gui
作者单位	1.Beijing Information Science and Technology University; School of Applied Science 2.Ministry of Science and Technology; National Laboratory for Scientific Computing
推荐引用方式 GB/T 7714	Hua,Dong-Ying,Li,Xiang-Gui,Zhu,Jiang. A mass conserved splitting method for the nonlinear Schr?dinger equation[J]. Advances in Difference Equations,2012,2012(1).
APA	Hua,Dong-Ying,Li,Xiang-Gui,&Zhu,Jiang.(2012).A mass conserved splitting method for the nonlinear Schr?dinger equation.Advances in Difference Equations,2012(1).
MLA	Hua,Dong-Ying,et al."A mass conserved splitting method for the nonlinear Schr?dinger equation".Advances in Difference Equations 2012.1(2012).