Geometric Numerical Integration for Peakon b-Family Equations

doi:10.4208/cicp.171114.140715a

	Geometric Numerical Integration for Peakon b-Family Equations
	Cai, Wenjun 1,3; Sun, Yajuan2 ; Wang, Yushun 3
	2016
发表期刊	COMMUNICATIONS IN COMPUTATIONAL PHYSICS
ISSN	1815-2406
卷号	19 期号:1 页码:24-52
摘要	In this paper, we study the Camassa-Holm equation and the Degasperis-Procesi equation. The two equations are in the family of integrable peakon equations, and both have very rich geometric properties. Based on these geometric structures, we construct the geometric numerical integrators for simulating their soliton solutions. The Camassa-Holm equation and the Degasperis-Procesi equation have many common properties, however they also have the significant difference, for example there exist the shock wave solutions for the Degasperis-Procesi equation. By using the symplectic Fourier pseudo-spectral integrator, we simulate the peakon solutions of the two equations. To illustrate the smooth solitons and shock wave solutions of the DP equation, we use the splitting technique and combine the composition methods. In the numerical experiments, comparisons of these two kinds of methods are presented in terms of accuracy, computational cost and invariants preservation.
关键词	Symplectic integrator splitting method WENO scheme multisymplectic integrator peakon shockpeakon
DOI	10.4208/cicp.171114.140715a
语种	英语
资助项目	National Natural Science Foundation of China[11271357] ; National Natural Science Foundation of China[11271195] ; National Natural Science Foundation of China[41504078] ; CSC ; Foundation for Innovative Research Groups of the NNSFC[11321061] ; ITER-China Program[2014GB124005]
WOS研究方向	Physics
WOS类目	Physics, Mathematical
WOS记录号	WOS:000369088500002
出版者	GLOBAL SCIENCE PRESS
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/21888
专题	计算数学与科学工程计算研究所
通讯作者	Sun, Yajuan
作者单位	1.Univ Chinese Acad Sci, Key Lab Computat Geodynam, Beijing 100049, Peoples R China 2.Chinese Acad Sci, LSEC, Acad Math & Syst Sci, Beijing 100190, Peoples R China 3.Nanjing Normal Univ, Sch Math Sci, Jiangsu Prov Key Lab NSLSCS, Nanjing 210023, Jiangsu, Peoples R China
推荐引用方式 GB/T 7714	Cai, Wenjun,Sun, Yajuan,Wang, Yushun. Geometric Numerical Integration for Peakon b-Family Equations[J]. COMMUNICATIONS IN COMPUTATIONAL PHYSICS,2016,19(1):24-52.
APA	Cai, Wenjun,Sun, Yajuan,&Wang, Yushun.(2016).Geometric Numerical Integration for Peakon b-Family Equations.COMMUNICATIONS IN COMPUTATIONAL PHYSICS,19(1),24-52.
MLA	Cai, Wenjun,et al."Geometric Numerical Integration for Peakon b-Family Equations".COMMUNICATIONS IN COMPUTATIONAL PHYSICS 19.1(2016):24-52.