報(bào) 告 人：耿獻(xiàn)國(guó)

報(bào)告時(shí)間：2024年12月12日下午16：30-17：30

報(bào)告地點(diǎn)： 蓮花街校區(qū)惟德樓315會(huì)議室

報(bào)告人簡(jiǎn)介：鄭州大學(xué)數(shù)學(xué)與統(tǒng)計(jì)學(xué)院，二級(jí)教授，博士生導(dǎo)師，鄭州大學(xué)特聘教授。國(guó)務(wù)院政府特殊津貼專家，河南省優(yōu)秀專家，全國(guó)百篇優(yōu)秀博士學(xué)位論文指導(dǎo)老師。 從事的研究方向是可積系統(tǒng)及應(yīng)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等刊物上發(fā)表論文。主持2項(xiàng)國(guó)家自然科學(xué)基金重點(diǎn)項(xiàng)目和多項(xiàng)國(guó)家自然科學(xué)基金面上項(xiàng)目等。獲得河南省自然科學(xué)一等獎(jiǎng)和河南省科學(xué)技術(shù)進(jìn)步獎(jiǎng)二等獎(jiǎng)，所帶領(lǐng)的研究團(tuán)隊(duì)被評(píng)為河南省可積系統(tǒng)及應(yīng)用研究創(chuàng)新型科技團(tuán)隊(duì)。

報(bào)告內(nèi)容簡(jiǎn)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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數(shù)學(xué)與統(tǒng)計(jì)學(xué)院
2024年12月12日