广义Caudrey-Dodd-Gibbon 方程及变系数Benney 方程的群分析 Alternative Title Group analysis of generalized Caudrey-Dodd-Gibbon equation and Benney equation with variable coefficients 卜文华 Thesis Advisor 周宇斌 2011-05-28 Degree Grantor 兰州大学 Place of Conferral 兰州 Degree Name 硕士 Keyword 广义Caudrey-Dodd-Gibbon 方程 变系数Benney 方程 经典对称 最优系统 约化方程 精确解 Abstract 非线性科学已经被广泛应用到各个学科, 例如: 生物学、物理学、化学、医学、经济学等等. 这些学科中涌现出的大量的非线性系统使非线性方程以及精确解的研究等问题变得尤为重要. 同时由于对称及守恒律的存在, 对称性研究已经变成一个非常重要的课题. 在本文中, 直接利用经典李群分析法来探讨两类发展方程的最优系统、约化方程以及精确解等问题. 首先, 将经典李群分析法应用到广义Caudrey-Dodd-Gibbon(CDG) 方程中, 并得到了该方程的经典李对称和最优系统. 且借助于(G′/G)-展开法求出了方程的精确解. 其次讨论了变系数Benney 方程的群分析, 并得到了该方程的最优系统和约化方程. 通过解特征方程, 不变量的方式, 最终获得了原始方程一些情况下的精确解. 最后给出文章的总结. Other Abstract The nonlinear science is widely applied in nature sciences, such as biology, physics, chemistry, medical science, economics and so on. The nonlinear system which emerges in these disciplines makes the research of nonlinear equations and exact solutions particularly important. And because the existence of symmetries and conservation laws, symmetry research has become an important topic. In this paper, we directly use classic lie group method to discuss optimal systems, reduction equations and exact solutions of two kinds of evolution equations. First, we study the classical symmetries of generalized Caudrey-Dodd- Gibbon(CDG) equation by classical Lie group method, getting the invariant groups and optimal systems. We directly seek for exact solutions of generalized CDG equation by (G′/G)-expansion method. Second, we discuss group analysis of Benney equation with variable coefficients. We get the optimal systems and the reduced equations of it. By solving the character equations and the invariants, eventually some exact solutions of it in some cases are obtained. Finally, we give a summery of this paper. URL 查看原文 Language 中文 Document Type 学位论文 Identifier https://ir.lzu.edu.cn/handle/262010/225317 Collection 数学与统计学院 Recommended CitationGB/T 7714 卜文华. 广义Caudrey-Dodd-Gibbon 方程及变系数Benney 方程的群分析[D]. 兰州. 兰州大学,2011.
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