The existence of solitary wave solutions of perturbed delayed Camassa-Holm equation


主讲人:杜增吉 江苏师范大学教授 博士生导师




主讲人先容: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,江苏省优秀教育工编辑,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Journal  of Functional Analysis, Journal of Differential Equations, Communications in  Contemporary Mathematics, Journal of Mathematical Biology  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。

内容先容: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.

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