报告题目 (Title)：Drinfel'd--Sokolov 方程族的可积（半）离散
报告人 (Speaker)：傅蔚 副教授（华东师范大学）
报告时间 (Time)：2021年11月29日(周一) 14:00-15:30
报告地点 (Place)：宝山校区G-507
主办部门：理学院数学系
报告摘要：We propose a novel semi-discrete Kadomtsev--Petviashvili equation with two discrete and one continuous independent variables, which is integrable in the sense of having the standard and adjoint Lax pairs, from the direct linearisation framework. By performing reductions on the semi-discrete Kadomtsev--Petviashvili equation, new semi-discrete versions of the Drinfel'd--Sokolov hierarchies associated with Kac--Moody Lie algebras $A_r^{(1)}$, $A_{2r}^{(2)}$, $C_r^{(1)}$ and $D_{r+1}^{(2)}$ are successfully constructed. A Lax pair involving the fraction of $\mathbb{Z}_\mathcal{N}$ graded matrices is also found for each of the semi-discrete Drinfel'd--Sokolov equations. Furthermore, the direct linearisation construction guarantees the existence of exact solutions of all the semi-discrete equations discussed in the paper, providing more insights into their integrability in addition of the analysis of Lax pairs.