讲座题目：The Sylvester equation and Ablowitz-Kaup-Newell-Segur system 主讲人：赵松林 副教授 开始时间：2019-09-10 13:00:00 结束时间：2019-09-10 14:00:00 讲座地址：数学馆201 主办单位：软件工程学院 报告内容： 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. |
