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博学堂讲座预告(第473讲)

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报告时间地点: 2019年11月30日 上午9:10-9:50  朝晖校区  教408
报告人: 张丹达博士      宁波大学
题目:Multi-component CAC systems

摘要:In this talk an approach to generate multi-dimensionally consistent N-component systems is proposed. The approach starts from scalar multi-dimensionally consistent quadrilateral systems and makes use of cyclic group.

The obtained N-component systems inherit integrable features such as Backlund transformations and Lax pairs, and exhibit many interesting aspects, such as nonlocal reductions. Higher order single component lattice equations (on larger stencils) and multi-component discrete Painleve equations can also be derived

in the context, and the approach extends to N-component generalizations of multi-dimensionally consistent 3D lattice equations.
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报告时间地点: 2019年11月30日 上午10:00-10:40  朝晖校区  教408
报告人: 傅蔚博士      华东师范大学
题目: Direct linearization approach to discrete integrable systems associated with $\mathbb{Z}_\mathcal{N}$ graded Lax pairs

摘要: Fordy and Xenitidis [J. Phys. A: Math. Theor. 50 (2017) 165205] recently proposed a large class of discrete integrable systems which include a number of novel integrable difference equations, from the perspective of $\mathbb{Z}_\mathcal{N}$ graded Lax pairs, without providing solutions. In this talk, we establish the link between the Fordy--Xenitidis discrete systems in coprime case and linear integral equations in certain form, which reveals solution structure of these equations. The bilinear form of the Fordy--Xenitidis integrable difference equations is also presented together with the associated general tau function. Furthermore, the solution structure explains the connections between the Fordy--Xenitidis novel models and the discrete Gel'fand--Dikii hierarchy.