报告题目：The Cauchy problem of vector complex modified Korteweg-de Vries equation: Large-time asymptotics with decaying initial data
报告摘要：In this talk, I will introduce the long-time asymptotic behavior of the solution to the Cauchy problem of the vector complex modified Korteweg-de Vries equation with a (m+1)*(m+1) matrix Lax pair on the line in the case of decaying initial data. With the nonlinear steepest descent method of Deift and Zhou for oscillatory Riemann-Hilbert problems, we demonstrate that, asymptotically in time, the (x,t)-plane primarily divides into three distinct regions: a left slow-decaying region where the asymptotics has the form of Zakharov--Manakov type, a central Painleve region where the asymptotics is characterized by the solution to a system of coupled Painleve II equations, which is connected to a (m+1)*(m+1) matrix RH problem and appears in a variety of random matrix models, and a right fast-decaying region. This is a joint work with Ran Wang.
报告时间：2025年5月16日上午10:00
报告地点：数学与统计学院学术报告厅D07
邀 请 人：孙晋易 教授
届时欢迎广大师生参与交流！
报告人简介
刘男，南京信息工程大学副教授，主要从事可积系统理论方法研究，包括反散射理论及可积系统解的长时间渐近分析，先后主持国家自然科学基金青年项目、江苏省自然科学基金青年项目、中国博士后科学基金特别资助和面上项目等研究课题，相关结果发表在J. Differential Equations、Phys. D、Stud. Appl. Math.、Sci. China Math.等重要学术期刊。
甘肃省数学与统计学基础学科研究中心
数学与统计学院
