讲座题目：Analytical Cartesian solutions of the multi-component Camassa-Holm equations 主讲人🚴：安红利 教授 主持人：陈勇 开始时间：2020-10-19 13:00:00 结束时间🧻：2020-10-19 14:00:00 讲座地址：腾讯会议 ID：412 906 192 主办单位：数学科学学院
报告人简介： 安红利，南京农业大学教授，博士。荣获钟山学者——学术新秀，江苏高校“青蓝工程”优秀骨干青年教师𓀑。
报告内容🥫💛： Here, we give the existence of analytical Cartesian solutions of the multi-component Camassa-Holm (MCCH) equations.Such solutions can be explicitly expressed, in which the velocity function is given by u=b(t)+A(t)x and no extra constraint on the dimension N is required. The advantage of our method is that we turn the process of analytically solving MCCH equations into algebraically constructing the suitable matrix A(t). As the applications, we obtain some interesting results: 1) If u is a linear transformation on x ∈ , then p takes a quadratic form of x. 2) If A = f(t)I +D with = −D, we obtain the spiral solutions. When N = 2, the solution can be used to describe “breather-type” oscillating motions of upper free surfaces. 3) If A = we obtain the generalized elliptically symmetric solutions. When N = 2, the solution can be used to describe the drifting phenomena of the shallow water flow. |
