报告题目:An insight into the q-difference two-dimensional Toda lattice equation, q-difference sine-Gordon equation and their integrability

报告人：李春霞 教授 首都师范大学

报告时间：2022年05月07日 上午09:30---10:30

报告地点：腾讯会议 会议ID：281578447

报告地点：腾讯会议 https://meeting.tencent.com/dm/2JglipgzrCuQ

会议ID：281578447 

摘要：In this paper, we first propose a generalized bilinear Backlund transformation and thus a generalized Lax pair for the bilinear q-difference two-dimensional Toda lattice (q-2DTL) equation. Next, starting from the known Darboux transformation for the noncommutative q-2DTL equation, we construct the existing Casoratian solutions to the bilinear q-2DTL equation and its bilinear Backlund transformation obtained by Hirota's bilinear method. And then, we successfully construct the binary Darboux transformation for the q-2DTL equation, based on which, Grammian solutions expressed in terms of quantum integrals are established for both the bilinear q-2DTL equation and its bilinear Backlund transformation. This reveals the profound connections between Darboux transformation and Hirota's bilinear method. In the end, by considering the 2-periodic reductions on the corresponding results of the q-2DTL equation, a q-difference sine-Gordon equation, a modified q-sG equation and their solutions are reported for the first time.

报告人简介：李春霞，首都师范大学数学科学学院教授。2005年中科院数学院计算数学所博士毕业，研究方向为数学物理。2005年-2007年在清华大学做博士后，2007-2008年受英国皇家学会资助在英国格拉斯哥大学从事博士后研究工作。先后作为国家公派留学人员和访问学者访问英国剑桥大学牛顿数学科学研究所、美国University of South Florida和College of Charleston。先后主持国家自然科学基金面上项目2项、青年基金项目1项，北京市自然科学基金面上项目2项等。目前主要研究经典可积系统和非交换可积系统的构造和可积性质、可积系统与正交多项式、可积系统与矩阵模型和随机矩阵理论中的矩阵积分等不同数学领域的交叉。部分研究工作发表在本领域认可度较高的杂志Journal of Nonlinear Science, Proceedings of the Royal Society A, Journal of Physics A和Inverse Problems等。

邀请人：任 博