报告题目 (Title)：聚焦NLS方程双极点存在下的稀疏问题的长时间行为（Long-time behaviors of the focusing nonlinear Schrödinger equation rarefaction problem in presence of double pole）

报告人 (Speaker)：王灯山 教授（北京师范大学数学科学学院）

报告时间 (Time)：2023年10月17日(周二) 14:00

报告地点 (Place)：腾讯会议：213-138-646

邀请人(Inviter)：夏铁成

主办部门：理学院数学系

报告摘要： This paper concerns the long-time behaviors of the focusing nonlinear Schrödinger equation with two kinds of non-zero boundary conditions. One kind is the rarefaction problem and the other is step-like initial-value problem with vanishing boundary on one side. The analytic region of the reflection coefficient is found by studying the convergence of the Volterra integral equations. All possible locations of double poles associated with the spectral functions are established and five sectors are classified for each non-zero boundary condition, such as the dumbing sector, trapping sector, trapping/waking sector, transmitting/waking sector and transmitting sector. The long-time asymptotic behaviors for each sector are analyzed by Deift-Zhou nonlinear steepest-descent strategy for Riemann-Hilbert problems.