“数理论坛”第108期：Bifurcations of Travelling Wave Solutions for Fully Nonlinear Water Waves with Surface Tension in the Generalized Serre-Green-Naghdi Equations

报告题目

Bifurcations of Travelling Wave Solutions for Fully Nonlinear Water Waves with Surface Tension in the Generalized Serre-Green-Naghdi Equations

报告时间

2019年9月19日下午15：30

报告地点

东区综合楼A1404会议室

报告人

李继彬（华侨大学教授）

报告人

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.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科研项目等10余项，发表论文200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. 1987-2018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、新加坡等国家和香港,澳门，台湾等地区进行科研合作与学术交流。

报告摘要

For the generalized Serre-Green-Naghdi equations with surface tension, by using the methodologies of dynamical systems and singular traveling wave theory developed Li \& Chen [2007] to their travelling wave systems, in different parameter conditions of the parameter space, all possible bounded solutions (solitary wave solutions, kink wave solutions, peakons, pseudo-peakons and periodic peakons as well as compactons) are obtained. More than 26 explicit exact parametric representations are given. It is interesting to find that this fully nonlinear water waves equation has coexistence of uncountably infinitely many smooth solitary wave solutions or uncountably infinitely many pseudo-peakon solutions with periodic solutions or compacton solutions. Differing from the well-known peakon solution of the Camassa-Holm equation, the generalized Serre-Green-Naghdi equations have four new forms of peakon solutions.

邀请人

郭上江 教授

2019年9月16日