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

讲座时间 Datetime: 2022年5月18日，星期三，14:30-16:00

地点 Venue: 腾讯线上会议：908 216 530

主持人 Host：吴志伟

报告人 Speaker: 李春霞 

单位 Affiliation:首都师范大学  

报告摘要 Abstract:

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.