報 告 人：耿獻國 教授

報告題目：Application of tetragonal curves to coupled Boussinesq equations

報告時間：2025年4月21日（周一）下午3:30

報告地點：靜遠樓1506學術報告廳

主辦單位：數學與統計學院、數學研究院、科學技術研究院

報告人簡介：

       耿獻國，鄭州大學數學與統計學院二級教授，博士生導師，國務院政府特殊津貼專家，全國百篇優秀博士學位論文指導老師。 長期從事可積系統理論及應用研究，在Commun. Math. Phys., Trans. Amer. Math. Soc., Adv. Math., J. Nonlinear Sci., SIAM J. Math. Anal., Int. Math. Res. Not. IMRN, Nonlinearity等刊物上發表論文。作為項目負責人，主持2項國家自然科學基金重點項目及多項面上項目。榮獲河南省自然科學一等獎和河南省科學技術進步獎二等獎。其領銜的可積系統及應用研究團隊入選河南省創新型科技團隊，在非線性科學領域具有重要學術影響力。

報告摘要：

       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.