报告题目 (Title)：四方曲线与Hirota-Satsuma方程的代数几何解
报告人 (Speaker)：耿献国 教授（郑州大学）
报告时间 (Time)：2021年11月21日(周日) 10:00-12:00
报告地点 (Place)：腾讯会议ID：143 198 989
邀请人(Inviter)：张大军
报告摘要：On the basis of the characteristic polynomials of Lax matrixes for the soliton hierarchies, we introduce the corresponding algebraic curves, including the hyperelliptic curve, trigonal curve, and tetragonal curve. We study the calculation of genus of algebraic curve, properties at infinity, and the construction of three kinds of Abel differentials. We establish the corresponding Baker-Akhiezer functions and meromorphic functions. The straightening out of various soliton flows is exactly given through the Abel map and Abel-Jacobi coordinates. Using the theory of algebraic curves, we obtain the explicit Riemann theta function representations of the Baker-Akhiezer function and the meromorphic function. As an illustration, we arrive at algebro-geometric solutions of the entire Hirota-Satsuma coupled hierarchy.