讲座题目：Analytical Cartesian solutions of the multi-component Camassa-Holm equations
开始来源：pt真人平台 时间：2020-10-19 13:00:00 结束来源：pt真人平台 时间：2020-10-19 14:00:00
讲座地址：腾讯会议 ID：412 906 192
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.