报告题目：Rigorous asymptotic analysis for the Riemann problem of the defocusing nonlinear Schrödinger hydrodynamics
报 告 人：王灯山
工作单位：北京师范大学
报告时间：2024-10-20 14:30-16:30
会议地点：vwin德赢AC米兰官网305
报告摘要：The long-time asymptotics for the defocusing nonlinear Schrödinger equation with step-like initial condition is investigated by the Riemann-Hilbert formulation. Whitham modulation theory shows that there are six cases for this initial discontinuity problem according to the orders of the Riemann invariants. We formulate the leading-order terms and the corresponding error estimates for each region of the six cases by Deift-Zhou nonlinear steepest-descent method. It is demonstrated that the asymptotic solutions match very well with the results from Whitham modulation theory and the 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2020-2023年中国高被引学者。
