报告题目:Asymptotic stability of solitary waves in shallow water models

报告人：王忠 副教授（佛山大学）

报告时间：12月12日（星期二）15:30-16:30

报告地点：腾讯会议：427-435-948

摘要：In this talk, I will report the asymptotic stability of smooth solitons and multi-solitons in energy space for the Camassa-Holm (CH) equation. We show that a CH solution initially close to a soliton, once translated, converges weakly in $H^1$, as time goes to infinity, to a possibly different soliton. The proof is motivated by the bi-Hamiltonian structure of the CH equation and a Liouville type theorem for the CH flow close to the solitons. The new ingredient in the proof of Liouville theorem is by employing the completeness relations of square eigenfunctions of the CH recursion operator. Some applications are presented in classifications of solutions of linear problems related to KdV and mKdV equations.

报告人简介：王忠，男，佛山大学数学系副教授，硕士生导师。研究非线性色散方程解的动力学行为和孤立子理论。法国巴黎综合理工学院和图卢兹第三大学访问学者。现为美国《数学评论》评论员,已主持包括国家青年基金，广东省面上基金等省部级以上项目4项。在CVPDE、Nonlinearity、JDE、Physica D和中国科学数学等期刊发表学术论文十余篇。