M?bius几何中的多分量Camassa-Holm方程
PDF下载 (271)覃 慧,王 宝.M?bius几何中的多分量Camassa-Holm方程[J].宁波大学学报(理工版),2023,36(3):43-49.DOI:
QIN Hui,WANG Bao.A multi-component Camassa-Holm equation arising from M?bius geometry[J].Journal of Ningbo University(Natural Science & Engineering Edition),2023,36(3):43-49.DOI:
| Title: | A multi-component Camassa-Holm equation arising from M?bius geometry |
| 作者: | 覃 慧, 王 宝 |
| Author(s): | QIN Hui, WANG Bao |
| 关键词: | 不变曲线流; M?bius几何; Camassa-Holm方程; 多分量Camassa-Holm系统; 尖峰孤子解 |
| Keywords: | invariant curve flow; M?bius geometry; Camassa-Holm equation; multi-component Camassa-Holm system; peaked solution |
| 分类号: | O29 |
| 文献标识码: | A |
| 摘要: | 研究了一般M?bius几何中的曲线流, 证明了一类多分量的Camassa-Holm方程等价于M?bius几何中的一个不变曲线流, 此方程是两分量Camassa-Holm方程的多分量推广, 也可以看成是一类多分量KdV系统的对偶可积系统. 最后得到了此方程的一个退化情形的尖峰孤子解. |
| Abstract: | In this paper, we study curve flows in general M?bius geometry, and prove that a class of multi-component Camassa-Holm equations are equivalent to an invariant curve flow in M?bius geometry, which is a multi-component generalization of the two-component Camassa-Holm equation, and can also be regarded as a dual integrable system of a class of multi-component KdV systems. We also obtain a peaked solution for a degradation case of multi-component Camassa-Holm equations. |
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| 备注/Memo: | 收稿日期:2022-11-08.宁波大学学报（理工版）网址:http://journallg.nbu.edu.cn/ 第一作者:覃慧（1996－）,女,广西桂平人,在读硕士研究生,主要研究方向:可积系统.E-mail:qhwbatg@163.com *通信作者:王宝（1990－）,男,河北保定人,讲师,主要研究方向:可积系统.E-mail:wangbao@nbu.edu.cn 宁波大学学报（理工版）网址：http://journallg.nbu.edu.cn/ |
