個(gè)人簡(jiǎn)介
耿獻(xiàn)國(guó), 理學(xué)博士，教授, 博士生導(dǎo)師。現(xiàn)任鄭州大學(xué)數(shù)學(xué)與統(tǒng)計(jì)學(xué)院院長(zhǎng), 中國(guó)數(shù)學(xué)會(huì)理事，河南省數(shù)學(xué)會(huì)理事長(zhǎng)。美國(guó)《數(shù)學(xué)評(píng)論》(Mathematical Reviews)和德國(guó)《數(shù)學(xué)文摘》(Zentralblatt Math)評(píng)論員。
研究方向
可積系統(tǒng)及應(yīng)用
獲獎(jiǎng)情況
獲國(guó)務(wù)院政府特殊津貼，河南省優(yōu)秀專家，河南省青年科技獎(jiǎng)，河南省自然科學(xué)優(yōu)秀論文一等獎(jiǎng)八項(xiàng)。河南省優(yōu)秀中青年骨干教師，河南省跨世紀(jì)學(xué)術(shù)與技術(shù)帶頭人。2012年獲教育部國(guó)務(wù)院學(xué)位委員會(huì): 全國(guó)優(yōu)秀博士學(xué)位論文指導(dǎo)教師。
基金項(xiàng)目
現(xiàn)主持國(guó)家自然科學(xué)基金重點(diǎn)項(xiàng)目一項(xiàng)和國(guó)家自然科學(xué)基金面上項(xiàng)目一項(xiàng)。主持完成國(guó)家自然科學(xué)基金項(xiàng)目五項(xiàng)和河南省杰出青年科學(xué)基金項(xiàng)目一項(xiàng)、河南省杰出人才計(jì)劃項(xiàng)目一項(xiàng)，承擔(dān)完成國(guó)家重點(diǎn)基礎(chǔ)性研究發(fā)展規(guī)劃(973規(guī)劃)子項(xiàng)目一項(xiàng)。
主要論文
1．X.G. Geng, Y.Y. Zhai and H.H. Dai, Algebro-geometric solutions of the coupled modified Korteweg-de Vries hierarchy, Advances in Mathematics 263 (2014) 123-153.
2．G.L. He, X.G. Geng, L.H. Wu, Algebro-geometric quasi-periodic solutions to the three-wave resonant interaction hierarchy, SIAM Journal on Mathematical Analysis 46, 2 (2014) 1348-1384.
3．X.G. Geng, LH. Wu and G.L. He, Quasi-periodic solutions of the Kaup-Kupershmidt hierarchy, Journal of Nonlinear Science 23, 4 (2013) 527-555.
4．X.G. Geng and H. Wang, Coupled Camassa-Holm equations, N-peakons and infinitely many conservation laws, Journal of Mathematical Analysis and Applications 403, 1 (2013) 262-271.
5．X.G. Geng, B. Xue, and LH. Wu, A super Camassau2013Holm equation with N-peakon solutions, Studies in Applied Mathematics 130, 1 (2013) 1-16.
6．X.G. Geng and D. Gong, Quasi-periodic solutions of the discrete mKdV hierarchy, International Journal of Geometric Methods in Modern Physics 10, 3 (2013) 1250094.
7．X.G. Geng and Y.Y. Lv, Darboux transformation for an integrable generalization of the nonlinear Schrodinger equation, Nonlinear Dynamics 69, 4 (2012) 1621-1630.
8．L.H. Wu, G.L. He and X.G. Geng, Quasi-periodic solutions to the two-component nonlinear Kleinu2013Gordon equation, Journal of Geometry and Physics 66 (2013) 1-17.
9．X.G. Geng, L.H. Wu and G.L. He, Algebro-geometric constructions of the modified Boussinesq flows and quasi-periodic solutions, Physica D：Nonlinear Phenomena 240, 16 (2011) 1262u20131288.
10．X.G. Geng and B. Xue, A three-component generalization of Camassa-Holm equation with N-peakon solutions, Advances in Mathematics 226, 1 (2011) 827-839.
11．X.G. Geng and B. Xue, Quasi-periodic solutions of mixed AKNS equations, Nonlinear Analysis: Theory, Methods & Applications 73, 11 (2010) 3662-3674.
12．X.G. Geng and B. Xue, Soliton solutions and quasiperiodic solutions of modified Korteweg-de Vries type equations, Journal of Mathematical Physics 51, 6 (2010) 063516.
13．X.G. Geng and L.H. Wu, A new super-extension of the KdV hierarchy, Applied Mathematics Letter 23, 6 (2010) 716u2013721.
14．X.G. Geng and B. Xue, An extension of integrable peakon equations with cubic nonlinearity, Nonlinearity 22, 8 (2009) 1847u20131856.
15．X.G. Geng, H.F. Ren and G.L. He, Darboux transformation for a generalized Hirota-Satsuma coupled Kortewegu2013de Vries equation, Physical Review E 79, 5 (2009) 056602.
16．X.G. Geng, H.H. Dai and J.Y. Zhu, Decomposition of the discrete Ablowitz- Ladik hierarchy, Studies in Applied Mathematics 118, 3 (2007) 281-312.
17．X.G. Geng and T. Su, Discrete coupled derivative nonlinear Schrodinger equations and their quasi-periodic solutions, Journal of Physics A: Math. Theor. 40, 3 (2007) 433-453.
18．X.G. Geng and H.H. Dai, Nonlinearization of the Lax pairs for discrete Ablowitzu2013Ladik hierarchy, Journal of Mathematical Analysis and Applications 327, 2 (2007) 829-853.
19．X.G. Geng, H.H. Dai and C.W. Cao, Algebrou2013geometric constructions of the discrete Ablowitzu2013Ladik flows and applications, Journal of Mathematical Physics 44, 10 (2003) 4573-4588.
20．X.G. Geng, Algebraic-geometrical solutions of some multidimensional nonlinear evolution equations, Journal of Physics A: Math. Gen. 36, 9 (2003) 2289-2303.
