9月10日:趙松林/孫瑩瑩/張丹達/陳奎
發布時間:2019-09-06  閱讀次數:1098

報告一:趙松林 

 

報告題目:The Sylvester equation and Ablowitz-Kaup-Newell-Segur system

報告人:趙松林 (浙江工業大學 副教授)

報告時間:2019年9月10日 周二13:00-14:00

報告地點:數學館201

 

報告摘要: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.

 

報告二:孫瑩瑩

報告題目:Modified Bäcklund transformations of the Boussinesq systems

報告人:孫瑩瑩 (上海理工大學 講師)

報告時間:2019年9月10日 周二14:00-15:00

報告地點:數學館201

 

報告摘要: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.

 

報告三:張丹達

 

報告題目:四邊格方程中的Bäcklund變換

報告人:張丹達 (寧波大學 講師)

報告時間:2019年9月10日 周二15:00-16:00

報告地點:數學館201

 

報告摘要:Bäcklund變換是方程間解的聯系,對于精確求解等有較好應用,因此Bäcklund變換的構造顯得尤為重要。目前國際上對于四邊格方程并無系統性構造方法。本報告將分別從多項式分解、周期函數的加法公式、立方體的對稱性三個角度來構造Bäcklund變換。最后建立Bäcklund變換與幾何的聯系。

 

報告四:陳奎 

報告題目:Bilinear equations and solutions for k-constrained D?KP

報告人:陳奎 (復旦大學 博士后)

報告時間:2019年9月10日 周二16:00-17:00

報告地點:數學館201

 

報告摘要: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.

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