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.