报告人：王忠（佛山大学）

（一）报告题目：Asymptotic stability of multi-solitons in shallow water models- part I -- integrability and square eigenfunctions

报告时间：2024年12月19日（星期四）14:15-16:15

报告地点：腾讯会议：478-587-790

（二）报告题目：Asymptotic stability of multi-solitons in shallow water models- part II -- the Camassa Holm Eq. and the modified Camassa Holm Eq.  

报告时间：2024年12月20日（星期五）15:30-17:00

报告地点：腾讯会议：978-740-445

报告摘要：In this talk, we shall briefly report a recent asymptotic stability result 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 to a possibly different soliton as time goes to infinity. 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. In the second part, I will disscuss also the orbital and asymptotic stability of N-solitons for the modified CH equation.  

邀请人：李骥

报告人简介：王忠，佛山大学科技处副处长，数学学院教授，硕士生导师。中山大学基础数学专业博士，法国巴黎综合理工学院和图卢兹第三大学访问学者。研究方向为非线性色散方程和孤立子稳定性理论。现为美国《数学评论》的评论员，广东省自然科学基金项目通讯评审专家。已主持国家自然科学基金青年科学基金项目1项，广东省自然科学基金面上项目2项。在CVPDE、Nonlinearity、JDE、Physica D和中国科学数学等学术期刊发表学术论文近二十篇，作为审稿专家审阅过JDE、Physica D、JPA和JMP等十余个数学物理期刊的学术论文。