张鸿庆
院系：数学科学学院
办公电话：**-8024
电子信箱：zhanghq@dlut.edu.cn
更新时间：2008-7-1
其他专业：应用数学



个人简介
1936年生于黑龙江省绥化县四方台镇，

1957年毕业于吉林大学数学系，同年至大连理工大学任教，

1980年任副教授，

1984年任教授，

1985年任美国Georgia Tech访问教授，

1987年回大连理工大学任教。


社会兼职
The editor of “Applied Mathematica and Mechanics”

研究领域（研究课题）
科研工作
1956年论文“一些特殊覆盖的不可能性”获吉林大学学生科学研究一等奖，中国青年报评价为“论文题目新颖有创造性”。

1979年论文“线性算子方程组一般解的代数构造”获辽宁省重大科技成果二等奖。光明日报、辽宁日报均有报道。成果被收入“教育部直属高等学校成果选编”，评价为“一百多年来，前人对弹性力学方程组、电动力学方程组的一般解往往只能适合一种特殊情况，不能推广。这一工作总结了弹性力学方程组的各种一般解，用代数的概念和构造方法，给出了统一理论和公式，并提出了恰当解这一重要概念，把过去弹性力学中应力函数位移函数的构造方法和其他场论问题联系起来，得到统一的求恰当解的方法，并推广到一般化的线性算子方程组理论中去。这个工作受到国内专家的好评，认为不仅是对基础理论的重要贡献，还有进一步推广的价值。在国外，这方面还未见到类似的工作。”

1987年因“多变量拟协调有限元法”的数学理论获国家自然科学奖三等奖，评语为“建立了以拟协调元方法为构架的更一般的有限元数学基础，进一步提出多变量有限元的逼近性，弱闭性、嵌入性、紧致性，比过去只基于位移元和和杂交元的数学基础，向前跨了一大步。”

1987年被授予辽宁省首批有突出贡献的中青年科技专家称号。

1988-1990年主持国家自然科学基金项目“有限元的数学理论及其应用”。

1989年成果被收入“国家自然科学基金资助项目优秀成果要览”。

1991年“辽河油田稠油层岩石热物理性参数计算方法研究”获辽宁省1991年科技进步二等奖。

1992-1994年主持国家自然科学基金项目：“求解连续体力学问题的微分代数和几何拓朴方法”。

1993-1997年为国家八五攀登计划项目：“机器证明及其应用”成员。

1996-1998年主持国家基金项目：“计算固体力学的辛算术代数几何模型”。

1998年为国家九五攀登预选项目‘数学机械化及其应用”成员。

1998-2003年为国家重点基础研究发展规划项目“数学机械化与自动推理平台”成员。

1999-2001年主持博士点基金项目：“力学问题求解的代数化对偶化体系”。

2001-2003年主持国家自然科学基金项目：“力学问题求解的代数化对偶化体系”。

2004-2009年为国家重点基础研究发展规划项目“数学机械化及其在信息科学中的应用”成员。

上世纪七十年代末以来，由国家首届最高科学技术奖获得者吴文俊先生倡导的数学机械化获得重要突破，居于世界领先地位。从1992年开始，张鸿庆教授一直是吴文俊先生领导的课题组成员，主要从事研究用数学机械化方法构造微分方程解析解，特别是非线性偏微分方程解析解，取得了一系列的成果。这些工作有以下特点：

1)具有统一的理论框架。构造微分方程的解析解是十分困难的工作，已构造出的解析解各有各的技巧，没有统一的方法，大量的重要问题无法求出解析解。张鸿庆教授提出一个统一的框架（AC=BD模式），既可以系统地产生已有的解，又能得到一系列新的解析解；

2)密切结合力学和物理。这些工作来自物理力学中的实际问题，弹性力学、电动力学、板壳理论、分析力学、流体力学、量子力学、超导、等离子体物理以及光纤通讯中的孤子理论等各个领域；

3)是数学机械化事业重要的组成部分。用统一的原理构造数学物理中机械化求解系统和机械化推理系统，以此为基础给出数学物理机械化统一的理论框架, 是数学机械化与力学中数学方法交汇的结果。一方面推动数学物理方法的现代化，另一方面是数学机械化思想的延伸和发展。数学物理机械化具有信息时代的特征，是历史发展的必然趋势。

4)研究范围从线性扩大到非线性。1996年以前的工作主要研究线性问题，96年以后重点转到非线性问题，原有的框架仍然适用，但内容有许多新的发展；

5)由于方向正确（主攻非线性，非线性问题是当前热点），框架统一（AC=BD模式），工具得力（计算机代数，符号计算），取得丰硕的成果，在中，俄，美，英，匈牙利，瑞典，新加坡, 日本，意大利，德国，荷兰，爱尔兰，保加利亚等十几个国家的各种SCI杂志上发表论文二百多篇，他引达千余次。

6)青年同志迅速成长。所指导学生获全国百篇优秀博士论文、省优秀博士论文各一篇；一名学生获首届宝钢优秀学生特等奖；一名学生在2002年SCI总数全国排名并列第一；一人获“中国卓越研究奖”。


硕博研究方向
1.数学机械化与数学物理；

2.偏微分方程求解及其应用.


出版著作和论文
专著:
1.“有限元的数学理论” 科学出版社1991.

2. Applications of mechanical methods to partial differential equations(chapter 17 of Mathematics Mechanization and Applications), Academic Press, NewYork ,2000.

3.泛函分析, 大连理工大学出版社, 2007.

4.流形上的微积分，大连理工大学出版社, 2007.

已发表部分论文：


1.Zhang Hongqing, Fan EG.,Applications of mechanical methods to partial differential equations,Mathematics Mechanization and Applications (17th chapter),Academic Press Limited(2000).

2.Zhang Hongqing,A united theory on general solutions of system of elasticity,J.Dalian Univ.Tech.,18(1978):25-47.

3.Zhang Hongqing,Algebraic constructions for general solutions of linear operator systems.Acta.Mech.Sinica(Special Issue): 152-161(1981).

4.Zhang Hongqing,Superfluous order and the proper solution of the Maxwell equation, Appl.Math.Mech,2(1981):349-360.

5.Zhang Hongqing, Wang Z., The completeness and approximation of Hu Haichang’s solution ,Kexue Tongbao ,1986 ,10:667-670.

6.Zhang, Hongqing ，C-D integrable system and computer aided solver for differential equations. Computer mathematics (Matsuyama, 2001), 221--226, Lecture Notes Ser. Comput., 9, World Sci. Publishing, River Edge, NJ, 2001.

7.Zhang Hongqing,Wu F.,General solution for a class of system of partial differential equations and its application in the theory of shells,Acta Mech.Sinica,24(1992):700-707.

8.Zhang Hongqing,Wu F.,General method for general solution of theory of plane and shell,Kexue Tongbao,13(1993):671-672.

9.Zhang Hongqing, The method for constructing general solution of system of partial differential equations,Proc.Comput..Mech.Tianjin Congr.,110-112(1991).

10.Zhang Hongqing, Hamiltonian representation for linear selfadjoint partial operators,Thirty years for nonholonomic mechanics in China,Henan Univ.Press,Kaifeng , 1994,182-186.

11.Zhang Hongqing, The algebraization , mechanization , symplectication and geometrization for mechanics , Modern Meth. And Mech.VII ,Shanghai Univ.Press ,Shanghai ,1997,20-25.

12.Zhang Hongqing,Chao L.,Operational form Hilbert Nukkstellensatz and symbolic algorithm for constructing general solution of system in elasticity , J. Dalian Univ.Tech.1996, ,36:373-379.

13.Zhang Hongqing, Chao L., Mathematica program package to compute symmetries of PDEs and its applications , Comput. Phys.,1997,14:375-379.

14.Zhang Hongqing,Chao L.,Exact algorithm of Taylor polynomial for symmetries of nonlinear partial differential equations,Appl. Math. Mech.,1998, 19:195-202.

15.Zhang Hongqing, Fan E.,Backlund transformation and exact solution for (2+1) dimensional KP equation , J. Dalian Univ.Tech. ,1997, 37:624-626.

16.Zhang Hongqing, Fan E., Linearization,similarity reduction and soliton solutions of KP equation in shallow water , J.Nonliear Dynamics ,1998, 5: 236-239.

17.Zhang Hongqing, Feng H., Algebraic structure of general solutions to system of nonhomogeneous linear operator equations , J. Dalian Univ.Tech. ,1994, 34:249-255.

18.Zhang Hongqing,Wu F., Mechanical method to construct the general solution for a system of partial differential equations,Proc.Int.Workshop Math.Mech.,Int.Academic Publ.,Beijing ,1992,280-285.

19.Zhang Hongqing,Wu F., The computational differential algebraic geometrical method for constructing the fundamental solution of partial differential equations,Proc.3rd Congr.Finete Element Method China ,Henan, China ,1992,183-191.

20.Wang Ming ,Zhang Hongqing, On the convergence of quasi-conforming elements for linear elasticity problem ,JCM ,Vol 4,No. 2, 131-145(1986).

21.Wang Ming ,Zhang Hongqing, The general Korn-Poincare inequality and its applications I ,Kexue Taosuo , Vol 2,No. 3, 83-92(1986).

22.Wang Ming ,Zhang Hongqing, A note on some finite element methods ,Comput.Math. , Vol 8,No. 3, 303-313(1986).

23.Wang Ming ,Zhang Hongqing, The finite element method of the stational Navier-Stokes system in plane , J. Dalian Univ.Tech. ,1986, 25:1-6.

24.Wang Ming ,Zhang Hongqing, Theembedded property andcompactness of the finite element space ,Appl. Math. Mech.,1988, 9:127-134.

25.Zhang Hongqing, The general patch test and 9-parameter quasi-conforming element ,Proc.the Sino-France Symposium on Finite Element Methods ,Science Press ,Gordan and Breach ,1983 ,566-583.

26.Zhang Hongqing, Wang Ming ,Finite elementapproximations with multiple sets of functions and quasi-conforming elements ,Proc.the 1984 Beijing Symp on Diff.Geometry and Diff.Equations ,,Science Press ,Beijing,1985 ,354-365.

27.Zhang Hongqing, Wang Ming ,Finite elementapproximations with multiple sets of functions and quasi-conforming elements ,Appl. Math. Mech.,1985, 6:41-52.

28.Zhang Hongqing, Wang Ming , thecompactness of quasi-conforming elements space and the convergence of quasi-conforming elements ,Appl. Math. Mech.,1986, 7:409-423.


29.Biao Li, Yong Chen and Hongqing Zhang, Explicit Exact Solutions for New General Two-dimensional KdV-type and Two-dimensional KdV-Burgers-type Equations with Nonlinear Terms of Any Order, J. Phys. A: Math. Gen., 35 (2002) 8253-8265.

30.Xuedong Zheng, Yong Chen and Hongqing Zhang, Generalized Extended Tanh-Function Methods and its Application to (1+1)-Dimensional Dispersive Long Wave Equation, Phys. Lett. A, 311 (2003) 145-157.

31.De-sheng Li and Hong-qing Zhang, Some new exact solutions of the integrable Broer–Kaup equations in (2+1)-dimensional spaces,(2003)Chaos, Solitons & Fractals,Volume 18, Issue 1,Pages 193-196.

32.De-sheng Li and Hong-qing Zhang, A further extended tanh-function method and new soliton-like solutions to the integrable Broer-Kaup (BK) equations in (2+1) dimensional spaces, Applied Mathematics and Computation 147 (2004) 537–545.

33.De-sheng Li and Hong-qing Zhang, A new extended tanh-function method and its application to the dispersive long wave equations in (2+1)- dimensions, Applied Mathematics and Computation 147 (2004) 789–797.

34.Huaitang Chen, Hongqing Zhang， Extended Jacobin elliptic function method and its applications. [Extended Jacobian elliptic function method and its applications，J.APPL.Math.Comput.，10 (2002) 119--130.

35.Huaitang Chen, Hongqing Zhang， Improved Jacobin elliptic function method and its applications. Chaos, Solitons and Fractals 15 (2003) 585--591.

36.Zhuosheng Lu , Hongqing Zhang, On a further extended tanh method. Phys.Lett.A， 307 (2003) 269--273.

37.Zhuosheng Lu , Hongqing Zhang, Soliton-like and period form solutions for high dimensional nonlinear evolution equations.Chaos, Solitons and Fractals 17 (2003) 669--673.

38.Zhuosheng Lu , Hongqing Zhang,Soliton like and multi-soliton like solutions for the Boiti–Leon–Pempinelli equation, Chaos, Solitons and Fractals 19 (2004) 527–531.

39.Yong Chen, Xuedong Zheng, Biao Li, Hongqing Zhang, New exact solutions for some nonlinear differential equations using symbolic computation, Applied Mathematics and Computation 149 (2004) 277–298.

40.Li, De-Sheng; Lü, Zhuo-Sheng; Zhang, Hong-Qing, Exact solutions of the (3+1)-dimensional KP and KdV-type equations. Commun. Theor. Phys. (Beijing) 39 (2003), no. 3, 267—270.

41.Zhang, Yu-Feng; Zhang, Hong-Qing，Solitary wave solutions for the coupled Ito system and a generalized Hirota-Satsuma coupled KdV system. Commun. Theor. Phys. (Beijing) 36 (2001), no. 6, 657--660.

42.XIA Tie-cheng, ZHANG Hong-qing, Generalized Numerical Radius of Real Quaternion Matrices with Symmetric Function, CHINESE QUARTERLY JOURNAL OF MATHEMATICS ,Vol. 15 　No. 3,34-38.

43.Zhang Yufeng,Zhang Hong qing, BACKLUND TRANSFORMATION AND SIMILARITYREDUCTIONSOF BOUSSINESQ EQUATION, Transactions of Nanjing University of Aeronautics&Astronautics,Vo l. 17. No. 2,199-202.

44.Alatancang,Zhang Hongqing,Zhong Wanxie, PSEUDO-DIVISION ALGORITHM FOR MATRIX MULTIVARIABLE POLYNOMIAL AND ITSAPPLICATION, Applied Mathematics and Mechanics,Vol . 21 , No. 7,733-740.

45.ZHANG Yu-feng , ZHANG Hong-qing, A FAMILY OF INTEGRABLE SYSTEMS OF LIOUVILLE AND LAX REPRESENTATION , DARBOUX TRANSFORMATIONS FOR ITS CONSTRAINED FLOWS, Applied Mathematics and Mechanics,Vol 23 , No 1,Jan 2002,26-34.

46.ZHANG Yu-feng, ZHANG Hong-qing, YAN Qing-you, Integrable couplings of Botie-Pempinelli-Tu (BPT) hierarchy, Physics Letters A 299 (2002) 543–548.

47.TONG Deng-ke，Zhang Hong-qing, THE FLOW PROBLEM OF FLUIDS FLOW IN A FRACTALRES ERVOIR WITH DOUBLE POROSITY, Applied Mathematics and Mechanics,Vol 22 , No 10,1118-1126.

48.FAN En-gui, ZHANG Hong-qing, A NEW COMPLETELY INTEGRABL ELIOUVILLE’S SYSTEM , ITS LAX REPRESENTATION AND BI-HAMILTONIAN STRUCTURE, Applied Mathematics and Mechanics,Vol 22 , No 5,520-527.

49.Xie, Fu Ding; Yan, Zhenya; Zhang, Hong Qing， Similarity reductions for the nonlinear evolution equation arising in the Fermi-Pasta-Ulam problem. Appl. Math. Mech. (English Ed.) 23 (2002), no. 4, 380--386;

50.Yan, Zhenya; Zhang, Hong Qing ，Multiple soliton-like and periodic-like solutions to the generalization of integrable (2+1)-dimensional dispersive long-wave equations. J. Phys.Soc. Japan 71 (2002), no. 2, 437--442.

51.Yan, Zhenya; Zhang, Hong Qing， A Lax integrable hierarchy, N-Hamiltonian structure, r-matrix, finite-dimensional Liouville integrable involutive systems, and involutive solutions. Chaos Solitons Fractals 13 (2002), no. 7, 1439--1450.

52.Yan, Zhenya; Zhang, Hong Qing， A new hierarchy of generalized derivative nonlinear Schrodinger equations, its bi-Hamiltonian structure and finite-dimensional involutive system. Nuovo Cimento Soc. Ital. Fis. B (12) 116 (2001), no. 11, 1255--1263.

53.Yan, Zhenya; Zhang, Hong Qing ，Symbolic computation and abundant new families of exact solutions for the coupled modified KdV-KdV equation. Computer mathematics (Matsuyama, 2001), 193--200, Lecture Notes Ser. Comput., 9, World Sci. Publishing, River Edge, NJ, 2001. 3

54.Yan, Zhenya; Zhang, Hong Qing， Study on exact analytical solutions for two systems of nonlinear evolution equations. Appl. Math. Mech. (English Ed.) 22 (2001), no. 8, 925--934;

55.Xia, Tie Cheng; Zhang, Hong Qing; Yan, Zhenya， New explicit and exact travelling wave solutions for a class of nonlinear evolution equations. Appl. Math. Mech. (English Ed.) 22 (2001), no. 7, 788--793;

56.Yan, Zhenya; Zhang, Hong Qing， New explicit solitary wave solutions and periodic wave solutions for Whitham-Broer-Kaup equation in shallow water. Phys. Lett. A 285 (2001), no. 5-6, 355--362.

57.Xie, Fuding; Yan, Zhenya; Zhang, Hong Qing， Explicit and exact traveling wave solutions of Whitham-Broer-Kaup shallow water equations. Phys. Lett. A 285 (2001), no. 1-2, 76--80.

58.Xia, Tie Cheng; Zhang, Hong Qing; Yan, Zhenya A new approach to constructing exact solutions of nonlinear evolution equations. (Chinese) J. Dalian Univ. Technol. 41 (2001), no. 3, 260--263.

59.Yan, Zhenya; Zhang, Hong Qing， Symbolic computation and new families of exact soliton-like solutions to the integrable Broer-Kaup (BK) equations in (2+1)-dimensional spaces. J. Phys. A 34 (2001), no. 8, 1785--1792.

60.Yan, Zhenya; Zhang, Hong Qing， A hierarchy of generalized AKNS equations, N-Hamiltonian structures and finite-dimensional involutive systems and integrable systems. J. Math. Phys. 42 (2001), no. 1, 330--339.

61.Yan, Zhenya; Zhang, Hong Qing ，Some conclusions for (2+1)-dimensional generalized KP equation: Darboux transformation, nonlinear superposition formula and soliton-like solutions. Computer mathematics (Chiang Mai, 2000), 239--248, Lecture Notes Ser. Comput., 8, World Sci. Publishing, River Edge, NJ, 2000.

62.Zhang, Hong Qing; Yan, Zhenya， Two types of new algorithms for finding explicit analytical solutions of nonlinear differential equations. Appl. Math. Mech. (English Ed.) 21 (2000), no. 12, 1423--1431;

63.Yan, Zhenya; Zhang, Hongqing， New explicit and exact travelling wave solutions for a system of variant Boussinesq equations in mathematical physics. Phys..Lett. A 252 (1999), no.6,291--296.



2005年到2008年部分论文：



64.Feng Y, Zhang HQ A new auxiliary function method for solving the generalized coupled Hirota-Satsuma KdV systemAPPLIED MATHEMATICS AND COMPUTATION Volume: 200 Issue: 1 Pages: 283-288

65.Yu FJ, Zhang HQ New Hamiltonian structure of the fractional C-KdV soliton equation hierarchy
66.CHAOS SOLITONS & FRACTALS Volume: 37 Issue: 3 Pages: 688-697

67.Yu FJ, Zhang HQ Hamiltonian structure of the integrable couplings for the multicomponent Dirac hierarchy APPLIED MATHEMATICS AND COMPUTATION Volume: 197 Issue: 2 Pages: 828-835

68.Yu FJ, Li L, Zhang HQ The multicomponent discrete equation hierarchy with variable spectral parameters and a new integrable coupling system PHYSICS LETTERS A Volume: 372 Issue: 11 Pages: 1750-1759

69.Song LN, Zhang HQ Application of the extended homotopy perturbation method to a kind of nonlinear evolution equations APPLIED MATHEMATICS AND COMPUTATION Volume: 197 Issue: 1 Pages: 87-95

70.Li WT, Zhang HQ Generalized multiple Riccati equations rational expansion method with symbolic computation to construct exact complexiton solutions of nonlinear partial differential equations APPLIED MATHEMATICS AND COMPUTATION Volume: 197 Issue: 1 Pages: 288-296

71.Zhi HY, Zhang HQ Symmetry analysis and exact solutions of (2+1)-dimensional Sawada-Kotera equation COMMUNICATIONS IN THEORETICAL PHYSICS Volume: 49 Issue: 2 Pages: 263-267

72.Yu F, Zhang HQ A new fractional order soliton equation hierarchy and its integrable coupling system APPLIED MATHEMATICS AND COMPUTATION Volume: 194 Issue: 1 Pages: 259-266

73.Yu FJ, Zhang HQ Fractional zero curvature equation and generalized Hamiltonian structure of soliton equation hierarchy INTERNATIONAL JOURNAL OF THEORETICAL PHYSICS Volume: 46 Issue: 12 Pages: 3182-3192

74.Wang Z, Zou L, Zhang HQ Applying homotopy analysis method for solving differential-difference equation PHYSICS LETTERS A Volume: 369 Issue: 1-2 Pages: 77-84

75.Zhang YY, Wang Q, Zhang HQ Negatons, positons, and complexiton solutions of higher order for a non-isospectral KdV equation COMMUNICATIONS IN THEORETICAL PHYSICS Volume: 48 Issue: 3 Pages: 411-414

76.Liu MY, Meng Y, Ren YL, et al. Nondestructive quantitative analysis of cofrel medicines by improved partial least squares-NIR spectroscopy SPECTROSCOPY AND SPECTRAL ANALYSIS Volume: 27 Issue: 6 Pages: 1098-1101

77.Wan Y, Song L, Yin L, et al.Generalized method and new exact wave solutions for (2+1)-dimensional Broer-Kaup-Kupershmidt system APPLIED MATHEMATICS AND COMPUTATION Volume: 187 Issue: 2 Pages: 644-657

78.Song L, Zhang HQ A new Korteweg-de Vries equation-based sub-equation method and its application to the (2+1)-dimensional Korteweg-de Vries equation APPLIED MATHEMATICS AND COMPUTATION Volume: 187 Issue: 2 Pages: 1368-1372

79.Song L, Zhang HQ New exact solutions for the Konopelchenko-Dubrovsky equation using an extended Riccati equation rational expansion method and symbolic computation APPLIED MATHEMATICS AND COMPUTATION Volume: 187 Issue: 2 Pages: 1373-1388

80.Song L, Zhang HQ New complexiton solutions of the nonlinear evolution equations using a generalized rational expansion method with symbolic computation APPLIED MATHEMATICS AND COMPUTATION Volume: 190 Issue: 1 Pages: 974-986

81.SongL, Zhang HQApplication of homotopy analysis method to fractional KdV-Burgers-Kuramoto equation PHYSICS LETTERS A Volume: 367 Issue: 1-2 Pages: 88-94

82.Zheng Y, Zhang YY, Zhang HQ Generalized Riccati equation rational expansion method and its application APPLIED MATHEMATICS AND COMPUTATION Volume: 189 Issue: 1 Pages: 490-499

83.Song LN, Zhang HQ A new variable coefficient Korteweg-de Vries equation-based sub-equation method and its application to the (3+1)-dimensional potential-YTSF equation APPLIED MATHEMATICS AND COMPUTATION Volume: 189 Issue: 1 Pages: 560-566

84.Wang D, Sun WW, Kong CC, et al.New extended rational expansion method and exact solutions of Boussinesq equation and Jimbo-Miwa equations APPLIED MATHEMATICS AND COMPUTATION Volume: 189 Issue: 1 Pages: 878-886

85.Song LN, Zhang HQ Extended Jacobi elliptic function rational expansion method and its application to (2+1)-dimensional stochastic dispersive long wave system COMMUNICATIONS IN THEORETICAL PHYSICS Volume: 47 Issue: 6 Pages: 969-974

86.Wang BD, Song LN, Zhang HQ A new extended elliptic equation rational expansion method and its application to (2+1)-dimensional Burgers equation CHAOS SOLITONS & FRACTALS Volume: 33 Issue: 5 Pages: 1546-1551

87.Huang DJ, Li DS, Zhang HQ Explicit N-fold Darboux transformation and multi-soliton solutions for the (1+1)-dimensional higher-order Broer-Kaup system CHAOS SOLITONS & FRACTALS Volume: 33 Issue: 5 Pages: 1677-1685

88.Yu FJ, Zhang HQ A new loop algebra system and its discrete integrable coupling system CHAOS SOLITONS & FRACTALS Volume: 33 Issue: 3 Pages: 829-834

89.Zhen W, Zhang HQ A method for constructing discrete exact solutions and application to quintic discrete nonlinear Schrodinger equation CHAOS SOLITONS & FRACTALS Volume: 33 Issue: 2 Pages: 642-652

90.Wang Q, Song LN, Zhang HQ A new coupled sub-equations expansion method and novel complexiton solutions of (2+1)-dimensional Burgers equation APPLIED MATHEMATICS AND COMPUTATION Volume: 186 Issue: 1 Pages: 632-637

91.Wang Z, Zhang HQ Many new kinds exact solutions to (2+1)-dimensional Burgers equation and Klein-Gordon equation used a new method with symbolic computation APPLIED MATHEMATICS AND COMPUTATION Volume: 186 Issue: 1 Pages: 693-704

92.Zhang XL, Zhang HQ A new generalized Riccati equation rational expansion method to a class of nonlinear evolution equations with nonlinear terms of any order APPLIED MATHEMATICS AND COMPUTATION Volume: 186 Issue: 1 Pages: 705-714

93.Zhi HY, Zhang HQNew rational solitary wave solutions of (2+1)-dimensional Burgers equation NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS Volume: 66 Issue: 10 Pages: 2264-2273

94.Zhi HY, Zhang HQ New formal solutions of Davey-Stewartson equation via combined tanh function method with symmetry method COMMUNICATIONS IN THEORETICAL PHYSICS Volume: 47 Issue: 4 Pages: 587-593

95.Yu FJ, Zhang HQ Upper triangular matrix of lie algebra and a new discrete integrable coupling system COMMUNICATIONS IN THEORETICAL PHYSICS Volume: 47 Issue: 3 Pages: 393-396

96.Ren YJ, Liu ST, Zhang HQ A new generalized algebra method and its application in the (2+1) dimensional Boiti-Leon-Pempinelli equation CHAOS SOLITONS & FRACTALS Volume: 32 Issue: 5 Pages: 1655-1665

97.Yu FJ, Zhang HQ A new Lie algebra to the multi-component Toda hierarchy and its discrete integrable coupling system CHAOS SOLITONS & FRACTALS Volume: 32 Issue: 3 Pages: 1053-1058

98.Zheng Y, Zhang YY, Zhang HQ A new general algebraic method with symbolic computation to construct new exact analytical solution for a (2+1)-dimensional cubic nonlinear Schrodinger equation CHAOS SOLITONS & FRACTALS Volume: 32 Issue: 3 Pages: 1101-1107

99.Huang DJ, Li DS, Zhang HQ Explicit and exact travelling wave solutions for the generalized derivative Schrodinger equation CHAOS SOLITONS & FRACTALS Volume: 31 Issue: 3 Pages: 586-593

100.Wang Z, Zhang HQ Soliton-like and periodic form solutions to (2+1)-dimensional Toda equation CHAOS SOLITONS & FRACTALS Volume: 31 Issue: 1 Pages: 197-204

101.Zhao XQ, Zhang HQ Interval oscillation criteria for a general class of second-order nonlinear differential equations with nonlinear damping and forcing term DYNAMICS OF CONTINUOUS DISCRETE AND IMPULSIVE SYSTEMS-SERIES A-MATHEMATICAL ANALYSIS Volume: 13 Pages: 91-95 Part: Part 1 Suppl. S Supplement: Part 1 Suppl. S

102.Zhang XL, Wang J, Zhang HQ A new generalized Riccati equation rational expansion method to generalized Burgers-Fisher equation with nonlinear terms of any order COMMUNICATIONS IN THEORETICAL PHYSICS Volume: 46 Issue: 5 Pages: 779-786

103.Mei JQ, Zhang HQ Potential symmetries and associated conservation laws to Fokker-Planck and burgers equation INTERNATIONAL JOURNAL OF THEORETICAL PHYSICS Volume: 45 Issue: 11 Pages: 2095-2102

104.Zhao XQ, Zhi HY, Zhang HQ Construction of doubly-periodic solutions to nonlinear partial differential equations using improved Jacobi elliptic function expansion method and symbolic computationCHINESE PHYSICS Volume: 15 Issue: 10 Pages: 2202-2209

105.Wang Z, Zhang HQNew exact solutions to some difference differential equations CHINESE PHYSICS Volume: 15 Issue: 10 Pages: 2210-2215

106.Ren YJ, Zhang HQ New generalized hyperbolic functions and auto-Backlund transformation to find new exact solutions of the (2+1)-dimensional NNV equation PHYSICS LETTERS A Volume: 357 Issue: 6 Pages: 438-448

107.Zhang YY, Zheng Y, Zhang HQ New complexiton solutions of (2+1)-dimensional Nizhnik-Novikov-Veselov equations COMMUNICATIONS IN THEORETICAL PHYSICS Volume: 46 Issue: 3 Pages: 407-414

108.Zhen W, Zhang HQ A symbolic computational method for constructing exact solutions to difference-differential equations APPLIED MATHEMATICS AND COMPUTATION Volume: 178 Issue: 2 Pages: 431-440

109.Yu R, Zhang HQ New function of Mittag-Leffler type and its application in the fractional diffusion-wave equation CHAOS SOLITONS & FRACTALS Volume: 30 Issue: 4 Pages: 946-955

110.Zheng Y, Zhang YY, Zhang HQ New extended Jacobi elliptic function rational expansion method and its application COMMUNICATIONS IN THEORETICAL PHYSICS Volume: 46 Issue: 1 Pages: 5-9

111.Song LN, Zhang HQ New exact solutions for Konopelchenko-Dubrovsky equation using an extended Riccati equation rational expansion method COMMUNICATIONS IN THEORETICAL PHYSICS Volume: 45 Issue: 5 Pages: 769-776

112.Yu FJ, Zhang HQ A new discrete integrable system and its discrete integrable coupling system CHAOS SOLITONS & FRACTALS Volume: 29 Issue: 5 Pages: 1173-1177

113.Huang DJ, Zhang HQ Link between travelling waves and first order nonlinear ordinary differential equation with a sixth-degree nonlinear term CHAOS SOLITONS & FRACTALS Volume: 29 Issue: 4 Pages: 928-941

114.Yu FJ, Zhang HQ New matrix Lie algebra, a powerful tool for constructing multi-component C-KdV equation hierarchy COMMUNICATIONS IN THEORETICAL PHYSICS Volume: 45 Issue: 4 Pages: 587-592

115.Huang DJ, Zhang HQNew exact travelling waves solutions to the combined KDV-MKDV and generalized Zakharov equations REPORTS ON MATHEMATICAL PHYSICS Volume: 57 Issue: 2 Pages: 257-269


116.Yu FJ, Zhang HQ A 2+1 non-isospectral discrete integrable system and its discrete integrable coupling system PHYSICS LETTERS A Volume: 353 Issue: 4 Pages: 326-331

117.Li DS, Zhang HQ A simple method for constructing elliptic function solutions to the nonlinear evolution equations and its applications ACTA PHYSICA SINICA Volume: 55 Issue: 4 Pages: 1565-1570

118.Yu R, Huang DJ, Zhang HQ Darboux transformation and new soliton-like solutions for (1+1)-dimensional higher-order Broer-Kaup system COMMUNICATIONS IN THEORETICAL PHYSICS Volume: 45 Issue: 3 Pages: 401-404

119.Zhang YY, Wang Q, Zhang H Q Further extended Jacobi elliptic function rational expansion method and new families of Jacobi elliptic function solutions to (2+1)-dimensional dispersive long wave equation COMMUNICATIONS IN THEORETICAL PHYSICS Volume: 45 Issue: 2 Pages: 199-206

120.Wang Z, Zhang HQ An algebraic method for constructing exact solutions to difference-differential equations COMMUNICATIONS IN THEORETICAL PHYSICS Volume: 45 Issue: 2 Pages: 211-218

121.Jiao XY, Zhang HQ An extended method and its application to Whitham-Broer-Kaup equation and two-dimensional perturbed KdV equation APPLIED MATHEMATICS AND COMPUTATION Volume: 172 Issue: 1 Pages: 664-677

122.Ren YJ, Zhang HQ A generalized F-expansion method to find abundant families of Jacobi Elliptic Function solutions of the (2+1)-dimensional Nizhnik-Novikov-Veselov equation CHAOS SOLITONS & FRACTALS Volume: 27 Issue: 4 Pages: 959-979

123.Yu FJ, Xia TC, Zhang HQ The multi-component TD hierarchy and its multi-component integrable coupling system with five arbitrary functions CHAOS SOLITONS & FRACTALS Volume: 27 Issue: 4 Pages: 1036-1041

124.Li DS, Zhang HQ A new method to construct Weierstrass elliptic function solutions for soliton equations ACTA PHYSICA SINICA Volume: 54 Issue: 12 Pages: 5540-5543

125.Zhang YY, Zheng Y, Zhang HQ New analytical solutions to the nonlinear Schrodinger equation model ZEITSCHRIFT FUR NATURFORSCHUNG SECTION A-A JOURNAL OF PHYSICAL SCIENCES Volume: 60 Issue: 11-12 Pages: 775-782

126.Jiang WY, Zhang HQ Soliton-like solutions to Wick-type stochastic mKdV equation COMMUNICATIONS IN THEORETICAL PHYSICS Volume: 44 Issue: 6 Pages: 981-986

127.Yu YX, Wang Q, Zhang HQ New explicit rational solitary wave solutions for discretized mKdV lattice equation COMMUNICATIONS IN THEORETICAL PHYSICS Volume: 44 Issue: 6 Pages: 1011-1014

128.Tong DK, Zhang HQ, Wang RH Exact solution and its behavior characteristic of nonlinear dual-porosity model APPLIED MATHEMATICS AND MECHANICS-ENGLISH EDITION Volume: 26 Issue: 10 Pages: 1277-1283

129.Wang DS, Liu YF, Zhang HQ Symbolic computation and families of Jacobi elliptic function solutions of the (2+1)-dimensional Nizhnik-Novikov-Veselov equation APPLIED MATHEMATICS AND COMPUTATION Volume: 168 Issue: 2 Pages: 823-847

130.Zhi HY, Zhao XQ, Zhang HQ New approach to find exact solutions to classical Boussinesq system COMMUNICATIONS IN THEORETICAL PHYSICS Volume: 44 Issue: 4 Pages: 597-603

131.Mei JQ, Zhang HQNew soliton-like and periodic-like solutions for the KdV equation APPLIED MATHEMATICS AND COMPUTATION Volume: 169 Issue: 1 Pages: 589-599

132.Huang DJ, Zhang HQ The extended first kind elliptic sub-equation method and its application to the generalized reaction Duffing model PHYSICS LETTERS A Volume: 344 Issue: 2-4 Pages: 229-237

133.Mei JQ, Zhang HQNew families of soliton and periodic solutions of Bose-Einstein Condensation in linear magnetic field and time-dependent laser field COMMUNICATIONS IN THEORETICAL PHYSICS Volume: 44 Issue: 2 Pages: 209-212

134.Wang DS, Zhang HQ Auto-Backlund transformation and new exact solutions of the (2+1)-dimensional Nizhnik-Novikov-Veselov equation INTERNATIONAL JOURNAL OF MODERN PHYSICS C Volume: 16 Issue: 3 Pages: 393-412

135.Zeng X, Zhang HQ New soliton-like solutions to the (2+1)-dimensional dispersive long wave equations ACTA PHYSICA SINICA Volume: 54 Issue: 2 Pages: 504-510

136.Mei JQ, Li DS, Zhang HQ New soliton-like and periodic solution of (2+1)-dimensional higher order Broer-Kaup systemCHAOS SOLITONS & FRACTALS Volume: 22 Issue: 3 Pages: 669-674

137.Mei JQ, Zhang HQ New types of exact solutions for a breaking soliton equation CHAOS SOLITONS & FRACTALS Volume: 20 Issue: 4 Pages: 771-777




工作成果（奖励、专利等）
1979年论文“线性算子方程组一般解的代数构造”获辽宁省重大科技成果二等奖。光明日报、辽宁日报均有报道。成果被收入“教育部直属高等学校成果选编”，评价为“一百多年来，前人对弹性力学方程组、电动力学方程组的一般解往往只能适合一种特殊情况，不能推广。这一工作总结了弹性力学方程组的各种一般解，用代数的概念和构造方法，给出了统一理论和公式，并提出了恰当解这一重要概念，把过去弹性力学中应力函数位移函数的构造方法和其他场论问题联系起来，得到统一的求恰当解的方法，并推广到一般化的线性算子方程组理论中去。这个工作受到国内专家的好评，认为不仅是对基础理论的重要贡献，还有进一步推广的价值。在国外，这方面还未见到类似的工作。”

1987年因“多变量拟协调有限元法”的数学理论获国家自然科学奖三等奖，评语为“建立了以拟协调元方法为构架的更一般的有限元数学基础，进一步提出多变量有限元的逼近性，弱闭性、嵌入性、紧致性，比过去只基于位移元和和杂交元的数学基础，向前跨了一大步。”

1987年被子授予辽宁省首批有突出贡献的中青年科技专家称号。

1989年成果被收入“国家自然科学基金资助项目优秀成果要览”。

1991年“辽河油田稠油层岩石热物理性参数计算方法研究”获辽宁省科技进步二等奖。



在读学生人数
博士 10名， 硕士11名

毕业学生人数
博士24名，硕士43名