Geometric Numerical Integration for Peakon b-Family Equations
文献类型：期刊论文
| 作者 | Cai, Wenjun1,3; Sun, Yajuan2 ; Wang, Yushun3
|
| 刊名 | COMMUNICATIONS IN COMPUTATIONAL PHYSICS
 |
| 出版日期 | 2016 |
| 卷号 | 19期号:1页码:24-52 |
| 关键词 | Symplectic integrator splitting method WENO scheme multisymplectic integrator peakon shockpeakon |
| ISSN号 | 1815-2406 |
| DOI | 10.4208/cicp.171114.140715a |
| 英文摘要 | 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. |
| 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 |
| 语种 | 英语 |
| WOS记录号 | WOS:000369088500002 |
| 出版者 | GLOBAL SCIENCE PRESS |
| 源URL | [http://ir.amss.ac.cn/handle/2S8OKBNM/21887]  |
| 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. |
入库方式： OAI收割
来源：数学与系统科学研究院
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