Tetragonal curves and algebro-geometric solutions of the Hirota-Satsuma coupled equations
数学公众报告
报告题目(Title)：Tetragonal curves and algebro-geometric solutions of the Hirota-Satsuma coupled equations
报告人(Speaker)：耿献国 教授（郑州大学数学与统计学院）
地点(Place)：腾讯会议：453 850 0147
时间(Time)：2021年11月13日(周六)，下午14:00-15:00
邀请人(Inviter)：王灯山
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.
主讲人简介
耿献国，二级教授，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，全国百篇优秀博士学位论文指导老师，曾任郑州大学数学与统计学院院长等职务。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. IMRN, 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。
