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数学与统计学院学术报告预告

发布日期:2024-12-12 作者: 阅读:

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

    人:耿献国

报告时间:20241212日下午1630-1730

报告地点:莲花街校区惟德楼315会议室


报告人简介:

耿献国,州大学数学与统计学院,二级教授,博士生导师,郑州大学特聘教授。国务院政府特殊津贴专家,河南省优秀专家,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., J. Nonlinear Sci., SIAM J. Math. Anal., Int. Math. Res. Not. IMRN, Nonlinearity等刊物上发表论文。主持2项国家自然科学基金重点项目和多项国家自然科学基金面上项目等。获得河南省自然科学一等奖和河南省科学技术进步奖二等奖,所带领的研究团队被评为河南省可积系统及应用研究创新型科技团队。

报告内容简介: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.

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