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耿献国教授
E-mail：xggeng@zzu.edu.cn
研究方向：可积系统及应用
个人简介:
博士，二级教授，博士生导师。现任郑州大学学科****—学科方向带头人，中国工业与应用数学会理事，河南省数学会理事长。美国《数学评论》(Mathematical Reviews)评论员。国务院政府特殊津贴专家，河南省专家。2003年被评为河南省****，2016年获河南省科技进步二等奖。2012年获全国百篇博士学位论文指导老师，所带领的研究团队2016年被评为河南省可积系统及应用研究创新型科技团队。
2005年2月至2017年3月任数学与统计学院院长, 中国数学会十届和十一届理事。
科研项目:
现主持1项国家自然科学基金重点项目。主持完成1项国家自然科学基金重点项目和多项国家自然科学基金面上项目，承担完成国家重点基础性研究发展规划（973规划）子项目。主持完成河南省****科学基金项目和河南省杰出人才计划项目。
主要发表论文:
J. Wei, X.G. Geng, X. Zeng, The Riemann theta function solutions for the hierarchy of Bogoyavlensky lattices, Transactions of the American Mathematical Society 371, 2 (2019) 1483-1507
X.G. Geng, X. Zeng, J. Wei, The application of the theory of trigonal curves to the discrete coupled nonlinear Schr?dinger hierarchy, Annales Henri Poincaré 20, 8 (2019) 2585–2621.
X.G. Geng and H. Liu, The nonlinear steepest descent method to long-time asymptotics of the coupled nonlinear Schr?dinger equation, Journal of Nonlinear Science 28, 2 (2018) 739-763
H. Liu, X.G. Geng, B. Xue, The Deift-Zhou steepest descent method to long-time asymptotics for the Sasa-Satsuma equation, Journal of Differential Equations 265, 11 (2018) 5984-6008
X.G. Geng and X. Zeng, Quasi-periodic solutions of the Belov-Chaltikian lattice hierarchy, Reviews in Mathematical Physics 29, 8 (2017) **, 27 pp.
X.G. Geng and H. Wang, Algebro-geometric constructions of quasi periodic flows of the Newell hierarchy and applications, IMA Journal of Applied Mathematics 82, 1 (2017) 97-130
X.G. Geng, H. Liu, J.Y. Zhu, Initial-boundary value problems for the coupled nonlinear Schr?dinger equation on the half-line, Studies in Applied Mathematics 135, 3 (2015) 310-346
L.H. Wu, X.G. Geng, J.S. Zhang, Algebro-geometric solution to the Bullough-Dodd-Zhiber-Shabat equation, International Mathematics Research Notices 2015, 8 (2015) 2141–2167
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.
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.
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.
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.
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.
X.G. Geng and B. Xue, N-soliton and quasi-periodic solutions of the KdV6 equations, Applied Mathematics and Computation 219, 8 (2012) 3504-351
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.
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.
X.G. Geng and B. Xue, An extension of integrable peakon equations with cubic nonlinearity, Nonlinearity 22, 8 (2009) 1847-1856.
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.
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