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

报告人：张大军教授，上海大学

报告时间：2023.11.06，10:30-11:30

报告地点：金融数学实验室

报告摘要：We establish a bilinear framework for elliptic soliton solutions which are composed by the Lamé-type plane wave factors and expressed using Weierstrass functions. The 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.

报告人简介：张大军，上海大学数学系教授，博士生导师。主要从事可积系统与数学物理的研究，在离散可积系统与椭圆函数、连续极限、多维相容性的应用、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6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。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(2012年至今)和国际期刊Journal of Physics A编委(2020年至今)。许多研究成果发表在《Communications in Mathematical Physics》、《Journal of Nonlinear Science》、《Journal of Physics A》、《Nonlinearity》等数学权威期刊上。

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