报告题目: Elliptic soliton solutions: tau functions, vertex operators and bilinear identities

报告人：张大军 教授

报告时间：2022年5月17日（周二）13：40-14:40

报告地点：腾讯会议 122 757 563

摘要：We establish a bilinear framework for elliptic soliton solutions of the KdV/KP type equations. These solutions are expressed using the Weierstrass functions and characterized by the Lamé-type plane wave factors. The bilinear framework includes elliptic soliton τ functions in Hirota’s form, vertex operators to generate τ functions and the associated bilinear identities. These are investigated in detail for the KdV equation and sketched for the KP hierarchy. Degenerations by the periods of elliptic functions are investigated, giving rise to the bilinear framework associated with trigonometric/hyperbolic and rational functions. Reductions by dispersion relation are also considered by employing the so-called elliptic N-th roots of the unity. The talk is based on a recent paper (joint with Xing Li (李幸)), arxiv: 2204.01240。

报告人简介：

张大军，上海大学数学系教授，博士生导师。目前主要研究非线性数学物理中的离散可积系统，长期国际合作单位包括Turku大学、Leeds大学、La Trobe大学等。目前指导博士生10位、硕士生5位。2002年上海大学获博士学位，先后作为国家公派留学人员和访问学者访问芬兰Turku大学、英国Leeds大学、剑桥牛顿数学研究所、美国Texas大学(RGV)、澳大利亚Sydney大学、La Trobe大学、日本早稻田大学等。2007年破格晋升教授。曾获上海市优秀博士学位论文，上海市高校优秀青年教师。先后主持国家自然科学基金面上项目5项、教育部博士点基金（博导类）1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(2006-2020)。目前担任国际系列会议SIDE (Symmetries and Integrability of Difference Equations)指导委员会委员(2012- )，国际期刊Journal of Physics A: Math. Theor. 编委（2020- ）。 

邀请人：赵松林