报告一：赵松林
报告题目：The Sylvester equation and Ablowitz-Kaup-Newell-Segur system
报告人：赵松林 (浙江工业大学 副教授)
报告时间：2019年9月10日 周二13:00-14:00
报告地点：数学馆201
报告摘要：In this talk, we seek connections between the Sylvester equation and the Ablowitz–Kaup–Newell–Segur (AKNS) system. By the Sylvester equation KM−MK = r sT, we introduce master function S(i,j ) = sT Kj (I + M)−1Ki r. This function satisfies some recurrence relations. By imposing dispersion relations on r and s, we study the constructions of the AKNS system, where some AKNS type equations are investigated emphatically, including second-AKNS equation, second-modified AKNS equation, third-AKNS equation, third-modified AKNS equation and first negative-AKNS equation. The reductions of these equations to complex Korteweg–de Vries equation, real and complex modified Korteweg–de Vries type equations, nonlinear Schrödinger type equations and sine-Gordon equation are discussed.
报告二：孙莹莹
报告题目：Modified Bäcklund transformations of the Boussinesq systems
报告人：孙莹莹 (上海理工大学 讲师)
报告时间：2019年9月10日 周二14:00-15:00
报告地点：数学馆201
报告摘要：It has been long understood how to interpret the permutability formula of the Bäcklund transformation as a lattice equation. I will talk about a recent result showing the lattice Boussinesq equation can be derived from a Bäcklund transformation of the potential Boussinesq system. This Bäcklund transformation is constructed through Weierstrass elliptic functions. I will then show how to obtain the elliptic seed and one soliton solution of the lattice Boussinesq equation.
报告三：张丹达
报告题目：四边格方程中的Bäcklund变换
报告人：张丹达 (宁波大学 讲师)
报告时间：2019年9月10日 周二15:00-16:00
报告地点：数学馆201
报告摘要：Bäcklund变换是方程间解的联系，对于精确求解等有较好应用，因此Bäcklund变换的构造显得尤为重要。目前国际上对于四边格方程并无系统性构造方法。本报告将分别从多项式分解、周期函数的加法公式、立方体的对称性三个角度来构造Bäcklund变换。最后建立Bäcklund变换与几何的联系。
报告四：陈奎
报告题目：Bilinear equations and solutions for k-constrained D∆KP
报告人：陈奎 (复旦大学 博士后)
报告时间：2019年9月10日 周二16:00-17:00
报告地点：数学馆201
报告摘要：The k-constrained D∆KP is investigated from views of the spectral problem, bilinear equations and solutions. These bilinear equations can be reduced to those of the k-constrained KP, on the reverse direction the solution of the k-constrained KP can be used to constructed the one of the k-constrained D∆KP. As example, the double Wronskian solution of the semi-discrete AKNS hierarchy is derived from the one of the AKNS hierarchy.
