报告题目：Long-time asymptotics of the Sawada-Kotera equation and Kaup-Kupershmidt equation on the line

报告人：王灯山教授(北京师范大学)

报告时间：2023年11月12日9:00-10:00

报告地点：数学与统计学院310会议室

报告摘要：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.

报告人简介：王灯山，北京师范大学数学科学学院，教授、博士生导师。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，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，曾获北京市自然科学奖二等奖(第一完成人)和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2020-2022年中国高被引学者。

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