报告时间：2022年04月28日（星期四）15:00-16:00

报告地点：腾讯会议：603459195

报 告 人：李春霞 教授

工作单位：首都师范大学

举办单位：数学学院

报告简介：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，博士生导师，研究方向为孤子理论与可积系统。中国科学院博士，清华大学博士后，格拉斯哥大学博士后（英国皇家学会资助）。访问剑桥大学牛顿数学科学研究所、美国University of South Florida和College of Charleston。曾主持国家自然科学基金项目3项、北京市自然科学基金面上项目2项等。曾在Journal of Nonlinear Science, Proceedings of the Royal Society A, Journal of Physics A和Inverse Problems等刊物上发表论文。