Algebraic curves and algebro-geometric solutions to soliton equations
报告人：耿献国教授（郑州大学）
报告时间：8月16日（周二）上午9:00-10:00
报告地点：腾讯会议：918 770 564
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 computation of the genus of these algebraic curves, the 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.
专家简介：
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。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。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., SIAM J. Math. Anal.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。
