关于举行郑州大学耿献国教授和薛波教授学术报告会的通知

报告题目1：Tetragonal curves and algebro-geometric solutions to the Satsuma-Hirota coupled hierarchy

报  告  人：耿献国  教授 (郑州大学)

报告时间：2021年 5月 6日（星期四）下午 15:00-16:00                

报告地点：腾讯会议，会议号：350 271 734

报告题目2：Some Applications of the steepest descent method to long-time asymptotics

报  告  人：薛波  教授 (郑州大学)

报告时间：2021年 5月 6日（星期四）下午 16:00-17:00                

报告地点：腾讯会议，会议号：350 271 734

邀  请  人：凌黎明  教授

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数学学院

2021年5月5日

报告摘要1：

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 Satsuma-Hirota coupled hierarchy.

报告摘要2：

The initial value problem for the Sasa–Satsuma equation is transformed to a 3×3 matrix Riemann–Hilbert problem with the help of the corresponding Lax pair. Two distinct factorizations of the jump matrix and a decomposition of the vector-valued function are given, from which the long-time asymptotics for the Sasa–Satsuma equation with decaying initial data is obtained by using the nonlinear steepest descent method .

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., 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。

        薛波，郑州大学数学与统计学院教授，博士生导师，现任数学与统计学院院长。国家级青年人才，全国优秀博士学位论文获得者，河南省中原青年拔尖人才，河南省学术技术带头人，享受河南省政府特殊津贴人员。薛波教授先后主持完成国家自然科学基金3项，教育部全国优秀博士学位论文作者专项资金资助项目1项，现正主持国家自然科学基金面上项目1项。在SCI学术期刊发表研究论文40余篇。