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(xué)術(shù)報告廳

主辦單位：數(shù)學(xué)與統(tǒng)計學(xué)院、數(shù)學(xué)研究院、科學(xué)技術(shù)研究院

報告人簡介：

       耿獻國，鄭州大學(xué)數(shù)學(xué)與統(tǒng)計學(xué)院二級教授，博士生導(dǎo)師，國務(wù)院政府特殊津貼專家，全國百篇優(yōu)秀博士學(xué)位論文指導(dǎo)老師。 長期從事可積系統(tǒng)理論及應(yīng)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(fā)表論文。作為項目負責人，主持2項國家自然科學(xué)基金重點項目及多項面上項目。榮獲河南省自然科學(xué)一等獎和河南省科學(xué)技術(shù)進步獎二等獎。其領(lǐng)銜的可積系統(tǒng)及應(yīng)用研究團隊入選河南省創(chuàng)新型科技團隊，在非線性科學(xué)領(lǐng)域具有重要學(xué)術(shù)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.