报 告 人：耿献国（郑州大学教授、博士生导师）
报告题目：四方曲线与孤子方程的代数几何解
报告时间：2021年04月29日上午11：00-11：40
报告地点：静远楼1506
主办单位：数学与统计学院、科学技术研究院
报告人简介：
耿献国，郑州大学数学与统计学院教授，博士生导师，郑州大学特聘教授。河南省数学会理事长，国务院政府特殊津贴专家，2012年获全国百篇优秀博士学位论文指导老师。从事的研究方向是可积系统及应用。曾在Commun. Math. Phys., Trans. Amer. Math. Soc., Adv. Math., J. Nonlinear Sci., SIAM J. Math. Anal., Int. Math. Res. Not., Nonlinearity等刊物上发表论文。主持国家自然科学基金重点项目2项和多项国家自然科学基金面上项目等。
报告摘要：
Using 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 Satsuma-Hirota coupled hierarchy.
邀请人：夏保强、张建兵