报告题目：Tau function, vertex operator and linearization scheme associated with Lamé function

报告地点：工程实训中心大楼1710

报告时间：2023年4月26日  下午15:00-16:30

报告简介：

Abstract: Elliptic curves can play a role in integrable systems, either as elliptic type solutions (i.e. solutions expressible in terms of elliptic functions), or as elliptic deformation of the equations themselves. In either way, the study of the elliptic case is often richer than the rational and trigonometric/hyperbolic cases, and reveals many new features of the models in question. The talk contains two parts. In the first part I will introduce 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 tau functions in Hirota’s form and the associated vertex operators and bilinear identities. These are introduced in detail for the KdV equation and sketched for the KP hierarchy. In the second part I will describe an elliptic direct linearisation scheme associated with discrete Lamé-type plane wave factors. This scheme allows us to have the lattice KP equations and lattice Boussinesq equations that have elliptic soliton solutions. In both continuous and discrete cases, the so-called elliptic N-th roots of unity are needed to define plane wave factors and implement reductions. Part I is based on a joint work with Xing Li and Part II based on a joint work with Frank Nijhoff and Yingying Sun.

报告人简介：

张大军，上海大学数学系教授，博士生导师。主要从事离散可积系统与数学物理的研究，包括离散可积系统的数学结构与直接方法、多维相容性的应用、空间离散下的可积结构与连续对应、可积系统与椭圆函数和椭圆曲线等。曾访问Turku大学、Leeds大学、剑桥牛顿数学研究所、Sydney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。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-)和期刊Journal of Physics A: Mathematical and Theoretical编委(2020- )。