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

doi:10.1186/1687-1847-2012-85

	A mass conserved splitting method for the nonlinear Schr?dinger equation
	Hua,Dong-Ying 1; Li,Xiang-Gui 1; Zhu,Jiang 2
刊名	Advances in Difference Equations
	2012-06-21
卷号	2012 期号:1
关键词	time-splitting finite difference dipolar Bose-Einstein condensates Schr?dinger equation conservation
ISSN号	1687-1847
DOI	10.1186/1687-1847-2012-85
英文摘要	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.
语种	英语
出版者	Springer International Publishing
WOS记录号	BMC:10.1186/1687-1847-2012-85
内容类型	期刊论文
源URL	[http://ir.amss.ac.cn/handle/2S8OKBNM/314]
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).