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Analytical Cartesian solutions of the multi-component Camassa-Holm equations
安红利 教授(南京农业大学)
2020年10月19日13:00-14:00  腾讯会议ID:412 906 192

*主持人:陈勇 教授
*时间:2020年10月19日13:00-14:00
*地点:腾讯会议ID:412 906 192

*讲座内容简介:
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.

*主讲人简介:
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。