我院硕士研究生刘磊同学与外校教授合作的三篇论文《Lie group classifications and exact solutions for two variable-coefficient equations》《Painlevé analysis, Lie symmetries, and exact solutions for the time-dependent coefficients Gardner equations》《Lie symmetry analysis, optimal systems and exact solutions to thefifth-order KdV types of equations》，已经分别被《Applied Mathematics and Computation》《Nonlinear Dynamics》《Journal of Mathematical Analysis and Applications》三本国际刊物采用并发表。这些刊物均获SCI（科学引文索引）全文收录，在数学界占有重要地位并具有广泛影响。
以下是这三本国际期刊的简介：
1. Nonlinear Dynamics（非线性动力学），SCI、EI收录期刊，编辑部位于美国，著名的德国Springer公司出版，主要发表微分方程与动力系统方面的研究成果，2009年影响因子1.658。
2. Journal of Mathematical Analysis and Applications（数学分析及应用），SCI、EI收录期刊，编辑部位于美国，著名的荷兰Elsevier出版公司出版，主要发表数学分析和应用数学方面的高水平研究成果，2009年影响因子1.225。
3. Applied Mathematics and Computation（应用数学与计算），SCI、EI收录期刊，编辑部位于美国，著名的荷兰Elsevier出版公司出版，主要发表应用数学与计算数学方面的研究成果，2009年影响因子1.124。
微分方程一直是现代数学的主要研究对象之一，在代数理论、工程力学及经济学诸领域中均有重要作用。现代金融数学与金融工程研究，一直依托于SDE（Stochastic Differential Equations，随机微分方程）作为其重要工具实现过程模拟、债券定价等计量分析，在此基础上建立严格而可操作的模型，以及对金融衍生品实现定价计算，均需要深厚的数学基础。除此三篇论文之外，刘磊同学在此领域仍有两篇参与完成的论文已获采用等待发表，另有与我院专职教师Ahmet Goncu博士（美国Florida State University）合作的两篇论文在工作中，充分证明了我院在金融学领域的研究已经处于国内领先水平。
以下是全部三篇论文的摘要：
Lie group classifications and exact solutions for two variable-coefficient equations
Applied Mathematics and Computation 215 (2009) 2927–2935
ABSTRACT
In this paper, the Lie symmetry analysis and group classifications are performed for two variable-coefficient equations, the hanging chain equation and the bond pricing equation. The symmetries for the two equations are obtained, the exact explicit solutions generated from the similarity reductions are presented. Moreover, the exact analytic solutions are considered by the power series method.
Painlevé analysis, Lie symmetries, and exact solutions for the time-dependent coefficientsGardnerequations
Nonlinear Dyn (2010) 59: 497–502
ABSTRACT
In this paper, the three variable-coefficient Gardner (vc-Gardner) equations are considered. By using the Painlevé analysis and Lie group analysis method, the Painlevé properties and symmetries for the equations are obtained. Then the exact solutions generated from the symmetries and Painlevé analysis are presented.
Lie symmetry analysis, optimal systems and exact solutions to the fifth-order KdV types of equations
J. Math. Anal. Appl. 368 (2010) 551–558
ABSTRACT
In this paper, the Lie symmetry analysis is performed on the fifth-order KdV types ofequations which arise in modeling many physical phenomena. The similarity reductionsand exact solutions are obtained based on the optimal system method. Then the exactanalytic solutions are considered by using the power series method.
