【讲座题目】聚焦非线性薛定谔方程相关的稀疏问题
【时 间】2022年10月8日 上午:9:00-10:00
【地 点】华北电力大学数理系 腾讯会议 ID:978-278-8659
【主 讲 人】王灯山 教授 北京师范大学
【主讲人简介】
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。
【报告内容简介】
In this talk, the long-time asymptotic behaviors of two separable plane waves of the focusing nonlinear Schrödinger equation in the presence of discrete spectrum are analyzed via the Riemann-Hilbert formulation. It is found that for large time there are four kinds of asymptotic regions in space-time frame, which includes the plane-wave region, plane-wave region with a phase shift from the discrete spectrum, the elliptic wave region with a one-phase wave and the cavitation region. The leading-order terms for these regions are computed with error estimates by using the Deift-Zhou steepest-descent method for Riemann-Hilbert problems. The numerical simulations match well with the theoretical analysis.