报告题目：Whitham modulation theory and Riemann problem of the Gerdjikov-Ivanov equation

报 告 人：王灯山 教授，北京师范大学

研究方向：数学物理，可积系统和渐近分析

报告时间：2024年1月13日（星期六）上午10:00

报告地点：量子楼410报告厅

报告摘要：

We develop the Whitham theory to study the Riemann problem of the Gerdjikov-Ivanov equation that describes the photon fluid with quintic nonlinearity. The one-phase periodic solution of the Gerdjikov-Ivanov equation and the corresponding Whitham equation are derived by the finite gap integration method. Subsequently, the main basic wave structures arising from the discontinuous initial-value conditions are found by distinguishing the distributions of the Riemann invariants. Some exotic optical undular bores are observed by classifying the solutions of the Riemann problem of the Gerdjikov-Ivanov equation. It is observed that the analytical results from Whitham theory are in excellent agreement with the numerical solutions.

报告人简介：

王灯山，北京师范大学，教授、博士生导师。主要从事数学物理，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2020-2022年中国高被引学者。