Long-time behaviors of the focusing NLS equation with nonzero boundary conditions at infinity in presence of double pole

王灯山  教授

（北京师范大学）

报告时间：2023年10月23日 (星期一) 下午14:30

报告地点: 沙河校区国实E502

报告摘要：This talk concerns the long-time behaviors of the focusing NLS equation with two kinds of non-zero boundary conditions at infinity. 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.

报告人简介：王灯山，北京师范大学154.com皇冠，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2020-2022年中国高被引学者。

邀请人： 王振

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