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On an integrable multi-component CamassaHolm system arising from Mbius geometry
Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences ( IF 2.9 ) Pub Date : 2021-07-28 , DOI: 10.1098/rspa.2021.0164
Jing Kang 1 , Xiaochuan Liu 2 , Changzheng Qu 3
Affiliation  

In this paper, we mainly study the geometric background, integrability and peaked solutions of a (1+n)-component Camassa–Holm (CH) system and some related multi-component integrable systems. Firstly, we show this system arises from the invariant curve flows in the Möbius geometry and serves as the dual integrable counterpart of a geometrical (1+n)-component Korteweg–de Vries system in the sense of tri-Hamiltonian duality. Moreover, we obtain an integrable two-component modified CH system using a generalized Miura transformation. Finally, we provide a necessary condition, under which the dual integrable systems can inherit the Bäcklund correspondence from the original ones.



中文翻译:

基于 Mbius 几何的可积多分量 CamassaHolm 系统

在本文中,我们主要研究了一个几何背景、可积性和峰值解。 (1+n)-分量 Camassa–Holm (CH) 系统和一些相关的多分量可积系统。首先,我们展示了这个系统是由莫比乌斯几何中的不变曲线流产生的,并且作为几何的对偶可积对应物(1+n)-分量 Korteweg-de Vries 系统在三汉密尔顿对偶的意义上。此外,我们使用广义 Miura 变换获得了一个可积的双组分改进 CH 系统。最后,我们提供了一个必要条件,在该条件下,对偶可积系统可以继承原始系统的 Bäcklund 对应关系。

更新日期:2021-07-28
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