主讲人：李继彬

主讲人简介：李继彬，华侨大学和浙江师范大学特聘教授，博士生导师，动力系统与非线性研究中心负责人，国家级突出贡献专家, 1991年获首届国务院特殊津贴。 曾任四届国家自然科学基金委数学学科评审专家组成员，云南省科学技术委员会常务委员， 三届云南省数学会理事长，云南省应用数学研究所副所长，昆明理工大学理学院院长等。 现为《应用数学与力学》等全国和国际性刊物的编委；美国《数学评论》与德国《数学文摘》评论员。主持承担国家自然科学基金重点项目和面上项目等10余项，发表论文230余篇，出版中英文专著10部，主编教材两部、出版科普书两本。科研成果曾分别获云南省和浙江省科学技术一等奖。 1987-2018年, 先后三十余次应邀到美国、俄国, 法国、加拿大、德国、英国等国家的多所大学和研究机构进行科研合作与学术交流。

报告内容概要：Water waves in channels and oceans are usually described by the Euler equations. Due to their complexity, several approximate models have been derived in various wave regimes. Indeed, considering long waves propagating in shallow water but without assuming small amplitudes, Serre derived a fully nonlinear weakly dispersive system of equations which, with some approximations, include the Korteweg-de Vries, Saint-Venant and Boussinesq equations as special cases. In 2010, Dias and Milewski presented a generalization of the Serre equations, which are fully-nonlinear, weakly dispersive and bidirectional (orisotropic) equations under a built-in assumption of irrotationality. It is very interesting that the corresponding traveling systems of these water wave models are singular traveling wave systems. In this talk, we state how to use the dynamical system approach to study the peakon, periodic peakon and compacton families for these water wave models.