Algebraic curves and algebro-geometric solutions to integrable nonlinear evolution equations

：耿献国（郑州大学）
：2022-11-22 09:00
：腾讯会议ID：466-005-8776（无密码）

报告人：耿献国（郑州大学）

时  间：11月22日上午09:00-10:30

地  点：腾讯会议ID：466-005-8776（无密码）

内容摘要:

On the basis of the characteristic polynomials of Lax matrices for the soliton hierarchies, we introduce the corresponding algebraic curves, including the hyperelliptic curve, trigonal curve, and tetragonal curve. We study the calculations of genuses for these algebraic curves, their 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.

个人简介：

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；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；主要研究领域是可积系统及其应用；在《Commun. Math. Phys.》、《Trans. Amer. Math. Soc.》、《Adv. Math.》、《J. Nonlinear Sci.》、《SIAM J. Math. Anal.》等刊物上发表130余篇论文；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，以及河南省杰出青年科学基金项目、河南省杰出人才计划项目等，承担完成国家重点基础性研究发展规划 (973规划)子项目。

 

联系人：李思泰