报告题目： On the theory and applications of singular nonlinear wave equations: dynamical system approach

报告人：李继彬教授  华侨大学

报告摘要：Nonlinear wave phenomena are of great importance in the physical world and have been for a long time a challenging topic of research for both pure and applied mathematicians. There are numerous nonlinear evolution equations for which we need to analyze the properties of the solutions for time evolution of the system. As the first step, we should understand the dynamics of their traveling wave solutions.

There exists an enormous literature on the study of nonlinear wave equations, in which exact explicit solitary wave, kink wave, periodic wave solutions, bifurcations and dynamical stabilities of these waves are discussed. To find exact traveling wave solutions for a given nonlinear wave system, a lot of methods have been developed such as the inverse scattering method, Darboux transformation method, Hirota bilinear method, algebraic-geometric method, tanh method, etc. What is the dynamical behavior of these exact traveling wave solutions?  How do the travelling wave solutions depend on the parameters of the system? What is the reason of the smoothness change of traveling wave solutions? How to understand the dynamics of the so-called compactons and peakon solutions? These are very interesting and important problems. In recent years, these topics have had significant advances and research is also very active.

The aim of this talk is to give a more systematic account for the bifurcation theory method of dynamical systems to find traveling wave solutions with an emphasis on singular waves and understand their dynamics for some classes of the well-posedness of nonlinear evolution equations.

报告时间：2018年4月7日(周六)下午2:00-2:50

报告地点：数学科学学院三楼专家接待室

欢迎教师和同学们参加！

李继彬教授简介：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220余篇,出版中英文专著8部,主编教材两本、出版科普书两部。三十余年培养硕士和博士研究生70余人。科研成果曾分别获云南省和浙江省科学技术一等奖。1987-2017年,先后三十余次应邀到美国、俄国、法国、加拿大、德国、英国、澳大利亚、西班牙、新加坡、南非等国家和香港、澳门、台湾等地区多所大学和研究机构进行科研合作与学术交流。