Möbius几何中的多分量Camassa-Holm方程  

A multi-component Camassa-Holm equation arising from Möbius geometry

作　　者：覃慧 王宝 QIN Hui;WANG Bao(School of Mathematics and Statistics,Ningbo University,Ningbo 315211,China)

机构地区：[1]宁波大学数学与统计学院,浙江宁波315211

出　　处：《宁波大学学报（理工版）》2023年第3期43-49,共7页Journal of Ningbo University：Natural Science and Engineering Edition

摘　　要：研究了一般Möbius几何中的曲线流,证明了一类多分量的Camassa-Holm方程等价于Möbius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.In this paper,we study curve flows in general Möbius geometry,and prove that a class of multi-component Camassa-Holm equations are equivalent to an invariant curve flow in Möbius 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.

关 键 词：不变曲线流 Möbius几何 CAMASSA-HOLM方程 多分量Camassa-Holm系统 尖峰孤子解 

分 类 号：O29[理学—应用数学]