讲座题目：On an integrable multi-component Camassa-Holm system arising from Mobius geometry 主讲人🪫：康静 教授 主持人：陈勇 教授 开始时间：2020-11-19 09:15:00 结束时间🏌️♀️：2020-11-19 10:30:00 讲座地址：腾讯会议 ID：600 742 617 主办单位🟪🦹🏿：数学科学学院
报告人简介： 康静，西北大学数学学院教授🐔、博导。主要研究方向为数学物理和非线性可积系统。具体的研究课题包括：对称和李群在微分方程中的应用、非线性可积系统可积性及孤立波解🏂、Liouville相关性理论及其应用。主持多项国家自然科学基金，一项陕西省自然科学基金杰出青年项目，入选“2017年度陕西省高校青年杰出人才支持计划”🙋🏿。
报告内容： In this talk, we study the geometric background, integrability and peaked solutions of a (1+n)-component Camassa-Holm (CH) system and some related multi-component integrable counterparts. We derive this multi-component CH system and its nonlocal μ-type version from the invariant curve flows in the Mobius geometry, and demonstrate that these two geometric systems are both integrable by establishing their bi-Hamiltonian structures as well as Lax-pair formulations respectively. We also investigate the peaked solutions for these two integrable systems. Moreover, we obtain an integrable (1+n)-component modified CH system, which admits the similar relationship with the geometric (1+n)-component CH system, in analogue to the relationship between the well-known CH and modified CH equations in scalar form. Finally, we prove a necessary condition, under which the dual integrable systems can inherit the Backlund correspondence from the original ones. The tri-Hamiltonian duality theory plays a key role in deriving the bi-Hamiltonian structures of the (1+n)-component (modified) CH systems. |
