报 告 人：耿献国 教授

报告题目：Application of tetragonal curves to coupled Boussinesq equations

报告时间：2025年4月21日（周一）下午3:30

报告地点：静远楼1506学术报告厅

主办单位：数学与统计学院、数学研究院、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二级教授，博士生导师，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。 长期从事可积系统理论及应用研究，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。作为项目负责人，主持2项国家自然科学基金重点项目及多项面上项目。荣获河南省自然科学一等奖和河南省科学技术进步奖二等奖。其领衔的可积系统及应用研究团队入选河南省创新型科技团队，在非线性科学领域具有重要学术影响力。

报告摘要：

       The hierarchy of coupled Boussinesq equations related to a 4×4 matrix spectral problem is derived by using the zero-curvature equation and Lenard recursion equations. The characteristic polynomial of the Lax matrix is employed to introduce the associated tetragonal curve and Riemann theta functions.The detailed theory of resulting tetragonal curves is established by exploring the properties of Baker–Akhiezer functions and a class of meromorphic functions. The Abel map and Abelian differentials are used to precisely determine the linearization of various flows. Finally, algebro-geometric solutions for the entire hierarchy of coupled Boussinesq equations are obtained.