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（首都师范大学数学学院）

报告时间：2022年10月20日下午2:30-3:30

报告地点：腾讯会议 607 251 870

报告摘要：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. In the end, by considering the 2-periodic reductions on the corresponding results of the q-2DTL equation, a q-difference.

邀请人：沈守枫