报告题目：The Riemann-Hilbert problem and long-time asymptotic analysis for the Yajima-Oikawa type integrable equations
报 告 人：王灯山 教授(北京师范大学)
报告时间：2026年03月30日，15:00开始
报告摘要：
Using the inverse scattering transform method, we prove that if a solution to the Yajima-Oikawa equation exists, it can be represented by the solution of a 3×3 matrix Riemann-Hilbert problem. Based on the constructed Riemann-Hilbert problem, we investigate the long-time behavior of solutions with generic initial data in Schwartz space, demonstrating that it takes the form of a finite sum of localized solitons and a dispersive component. The leading-order asymptotics of the solution is given by a multi-soliton solution whose parameters are slightly modified from their initial values due to soliton-soliton and soliton-radiation interactions. Our analysis provides an explicit expression for the corrective dispersive term.
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、Nonlinearity、J. Differential Equations和J. Nonlinear Science等国际期刊上发表学术论文100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。
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