High order symplectic schemes for the sine-Gordon equation

doi:10.1143/JPSJ.72.2731

CSpace

	High order symplectic schemes for the sine-Gordon equation
	Wang, YS ; Wang, B ; Ji, ZZ ; Qin, MZ
	2003-11-01
发表期刊	JOURNAL OF THE PHYSICAL SOCIETY OF JAPAN
ISSN	0031-9015
卷号	72 期号:11 页码:2731-2736
摘要	In this paper, taking the sine-Gordon equation as an example, we present a new method to construct the symplectic schemes for Hamilton PDEs. Different from the previous symplectic methods dealing with PDEs, our method is that to view the PDEs as a Hamilton system in Banach space, then to apply the generating functions method to the Hamilton system. After overcoming successfully the essential difficulties on the calculations of high order variation derivatives, we get the semi-discrete difference schemes for the PDEs with arbitrary order of accuracy in time direction. Furthermore the corresponding modified equations of the infinite dimensional Hamiltonian system are obtained from the semidiscretization. We use the central difference operators to discretize the derivatives in space. Thus the resulting full discrete symplectic schemes can be of any order accuracy. Numerical results on collisions of solitons are also presented to show the effectiveness of the schemes.
关键词	sine-Gordon equation high order symplectic scheme generating function method variation derivative
DOI	10.1143/JPSJ.72.2731
语种	英语
WOS研究方向	Physics
WOS类目	Physics, Multidisciplinary
WOS记录号	WOS:000186914400009
出版者	PHYSICAL SOC JAPAN
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/19119
专题	中国科学院数学与系统科学研究院
通讯作者	Wang, YS
作者单位	1.Chinese Acad Sci, Lasg, Inst Atmospher Phys, Beijing 100029, Peoples R China 2.Nanjing Normal Univ, Sch Math & Comp Sci, Nanjing 210097, Peoples R China 3.Chinese Acad Sci, Inst Computat Math, Acad Math & Syst Sci, Beijing 100080, Peoples R China
推荐引用方式 GB/T 7714	Wang, YS,Wang, B,Ji, ZZ,et al. High order symplectic schemes for the sine-Gordon equation[J]. JOURNAL OF THE PHYSICAL SOCIETY OF JAPAN,2003,72(11):2731-2736.
APA	Wang, YS,Wang, B,Ji, ZZ,&Qin, MZ.(2003).High order symplectic schemes for the sine-Gordon equation.JOURNAL OF THE PHYSICAL SOCIETY OF JAPAN,72(11),2731-2736.
MLA	Wang, YS,et al."High order symplectic schemes for the sine-Gordon equation".JOURNAL OF THE PHYSICAL SOCIETY OF JAPAN 72.11(2003):2731-2736.