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数学学科学术报告(杜增吉 江苏师范大学)

发布者:马俊   发布时间:2019-03-11  浏览次数:198

报告题目:The existence of solitary wave solutions of delayed Camassa-Holm equation  

报告时间:星期二,3月12日,下午3:30

报告地点:20-404 第一会议室

摘要:In this talk, we discuss the Camassa-Holm equation, which is a model for shallow water waves. We first establish the existence of solitary wave solutions for the equation without delay. And then we prove the existence of solitary wave solutions for the equation with a special local delay convolution kernel and a special nonlocal delay convolution kernel by using the method of dynamical system, especially the geometric singular perturbation theory and invariant manifold theory. According to the relationship between solitary wave and homoclinic orbit, the Camassa-Holm equation is transformed into the ordinary differential equations with fast variables by using the variable substitution. It is proved that the equation with disturbance also possesses homoclinic orbit, and there exists solitary wave solution of the delayed Camassa-Holm equation!

          杜增吉,江苏师范大学教授、博士、博士生导师、副校长,中国数学会奇异摄动专业委员会副理事长,江苏省“333高层次人才”中青年科学技术带头人,江苏省“青蓝工程”中青年学术带头人。研究方向为微分方程与动力系统、奇异摄动理论及其应用等。在J. Funct. Anal.,J. Differential Equations, Commun. Contemp. Math., J. Math. Biol. 等数学杂志上发表SCI论文60多篇,在科学出版社出版专著1部,主持国家自然科学基金和省部级项目10余项。