一、报告题目：Elliptic tau functions and vertex operators for the lattice potential KdV and KP

二、报告人：张大军 教授

三、时 间：2024年10月21日（周一）15:30-16:30

四、地 点：闻理园A4-305

报告摘要：The Lamé function can be used to construct plane wave factors and solutions to the Korteweg-de Vries (KdV) and Kadomtsev-Petviashvili (KP) hierarchies. The solutions are usually called elliptic solitons. In this talk, first, we review recent development in the Hirota bilinear method on elliptic solitons of the KdV equation and KP equation, including bilinear calculations involved with the Lamé type plane wave factors, expressions of tau functions and the generating vertex operators. Then, for the discrete potential KdV and KP equations, we give their bilinear forms, derive tau functions of elliptic solitons, and show that they share the same vertex operators with the KdV hierarchy and the KP hierarchy, respectively. [This talk is based on the paper with Xing Li, arxiv: 2307.02312]

报告人简介：张大军教授，上海大学数学系教授，博士生导师。主要从事离散可积系统与数学物理的研究，在离散可积系统的直接方法、多维相容性的应用、空间离散下的可积结构与连续对应、精确解的结构与应用等方面取得了有意义的学术成果。曾作为访问学者，访问Turku大学、Leeds大学、剑桥牛顿数学研究所、Sydney大学、早稻田大学等学术机构。先后主持国家自然科学基金面上项目和国际合作项目7项、参与国家自然科学基金重点项目1项。曾担任国际期刊Journal of Nonlinear Mathematical Physics编委。目前担任离散可积系统国际系列会议SIDE (Symmetries and Integrability of Difference Equations)指导委员会委员和国际期刊Journal of Physics A和Open Communications in Nonlinear Mathematical Physics编委。

欢迎大家参加！联系人：施英、杨云青