Academy of Mathematics and Systems Science, CAS
Colloquia & Seminars
| | Speaker: | 李春霞 教授，首都师范大学
| | Inviter: | | Title:
| Elementary and binary Darboux transformations to the q-difference two-dimensional Toda lattice equation | Time & Venue:
| 2021.11.19 14:30-15:30 腾讯会议 ID：783 424 600 | Abstract:
| As important extensions of the classical integrable systems, q-difference integrable systems are of great research interest. For the bilinear q-difference two-dimensional Toda lattice equation which can be reduced to the well-known two-dimensional Toda lattice equation by taking the continuum limit , Ohta etc. considered its Wronskian-type determinant solutions by using the bilinear method. However, other important integrable properties remain unknown. Recently, we managed to derive its Lax pair, construct its Wronskian-type determinant solutions by Darboux transformation, and Grammian-type determinant solutions expressed in terms of quantum integrals by binary Darboux transformation. In addition, we obtained Wronskian-type determinant solutions and Grammian-type determinant solutions to the bilinear Backlund transformation for the bilinear q-difference two-dimensional Toda lattice equation as well. In fact, as parts of the Darboux transformation and binary Darboux transformation, we found that the N-step iterations of eigenfunctions give nothing but two types of solutions to the bilinear Backlund transformation, respectively.
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