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Whitham modulation theory and the classification of solutions of the Riemann problem for the Fokas-Lenells equation

田守富 教授

报告时间：2025年01月07日（星期二）晚上7：00--8🧛🏿‍♂️：00

报告地点：腾讯会议：709-765-033

报告摘要：

In this work, we explore the Riemann problem of the Fokas-Lenells equation given initial data in the form of a step discontinuity by employing the Whitham modulation theory. The periodic wave solutions of the Fokas-Lenells equation are characterized by elliptic functions along with the Whitham modulation equations. Moreover, we find that the $\pm$ signs for the velocities of the periodic wave solutions remain unchanged during propagation. Thus, when analyzing the propagation behavior of solutions, it is necessary to separately consider the clockwise (negative velocity) and counterclockwise (positive velocity) cases. In this regard, we present the classification of the solutions to the Riemann problem of the Fokas-Lenells equation in both clockwise and counterclockwise cases for the first time.

报告人简介🦉：

田守富📂👴🏿，中国矿业大学数学凯发K8教授、博士生导师，2012年博士毕业于大连理工大学凯发娱乐，主要从事可积系统、反散射理论💂🏼‍♀️、Riemann-Hilbert问题🤧、渐近分析等的研究🥾；主持国家自然科学基金面上项目等多项研究课题；研究成果在《Adv. Math.》、《Math. Ann.》和《中国科学》等国内外期刊上发表学术论文多篇； 曾获辽宁省自然科学二等奖👩‍🦽‍➡️、淮海科技二等奖、江苏省科技奖三等奖☹️、淮海科技英才奖、江苏省数学会科技奖一等奖(原江苏省数学成就奖)和江苏省工业与应用数学学会青年科技奖等🤨；入选国家高层次青年人才计划🌓、江苏省“333工程”中青年科学技术带头人、江苏省“六大人才高峰”高层才人才计划和2020-2023连续四年爱思唯尔中国高被引学者等。

邀请人👰： 王振

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