【耿献国】郑州大学数学与统计学院研究生导师介绍

信息发布

　　E-mail：xggeng@zzu.edu.cn

　　研究方向：可积系统及应用

　　个人简介

　　耿献国，理学博士，教授, 博士生导师。现任郑州大学数学与统计学院院长, 中国数学会理事，河南省数学会理事长。美国《数学评论》(Mathematical Reviews)和德国《数学文摘》(Zentralblatt Math)评论员。

　　获奖情况

　　获国务院政府特殊津贴，河南省优秀专家，河南省青年科技奖，河南省自然科学优秀论文一等奖八项。河南省优秀中青年骨干教师，河南省跨世纪学术与技术带头人。2012年获教育部国务院学位委员会: 全国优秀博士学位论文指导教师。

　　基金项目

　　现主持国家自然科学基金重点项目一项和国家自然科学基金面上项目一项。主持完成国家自然科学基金项目五项和河南省杰出青年科学基金项目一项、河南省杰出人才计划项目一项，承担完成国家重点基础性研究发展规划(973规划)子项目一项。

　　主要发表论文

　　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 Camassa–Holm 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 Klein–Gordon 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) 1262–1288.

　　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) 716–721.

　　14．X.G. Geng and B. Xue, An extension of integrable peakon equations with cubic nonlinearity, Nonlinearity 22, 8 (2009) 1847–1856.

　　15．X.G. Geng, H.F. Ren and G.L. He, Darboux transformation for a generalized Hirota-Satsuma coupled Korteweg–de 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 Ablowitz–Ladik hierarchy, Journal of Mathematical Analysis and Applications 327, 2 (2007) 829-853.

　　19．X.G. Geng, H.H. Dai and C.W. Cao, Algebro–geometric constructions of the discrete Ablowitz–Ladik 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.