题目：Long-time asymptotics of the Sawada-Kotera equation and Kaup-Kupershmidt equation on the line
摘要：In this talk, we report our recent studies on the long-time asymptotics of the Sawada-Kotera (SK) equation and Kaup-Kupershmidt (KK) equation. Both SK equation and KK equation are integrable systems with third-order Lax operator. Moreover, they are related with the same modified nonlinear equation (called modified SK-KK equation) by Miura transformations. This work first constructs the Riemann-Hilbert problem associated with the SK equation, KK equation and modified SK-KK equation by direct and inverse scattering transforms. Then the long-time asymptotics of these equations are studied based on Deift-Zhou steepest-descent method for Riemann-Hilbert problem. Finally, it is shown that the asymptotic solutions match very well with the results of direct numerical simulations. This is a joint work with Xiaodong Zhu.
时间：2023年12月18日下午15:00
地点：中关村校区教学楼第二层N210
报告人简介：王灯山，理学博士，教授，博士生导师。2008年毕业于中国科学院数学与系统科学研究院，获博士学位。曾在中国科学院物理研究所和瑞典皇家理工学院从事博士后研究，美国杜克大学、加拿大多伦多大学和新加坡国立大学访问学者。主要从事可积系统和渐近分析方面的研究，在Analysis & PDE, Physical Review Letters, J. Differential Equations, J. Nonlinear Science 和Physica D等国际期刊发表学术论文90余篇（其中ESI高被引论文10篇），他引超过2300次；出版专著2部；主持国家自然科学基金面上项目等国家级和省部级项目10余项；曾获得茅以升北京青年科技奖，并参与获得北京市科学技术奖一等奖；入选北京市“科技新星”计划、北京市“高创计划”青年拔尖人才、北京市“长城学者”计划以及爱思唯尔2020、2021年中国高被引学者。
