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题名	李群方法在求解几类偏微分方程中的应用; The application of Lie group to the solution of several classical partial differential equations
作者	何再明
学位类别	硕士
答辩日期	2006-06-14
授予单位	中国科学院广州能源研究所
授予地点	广州能源研究所
导师	游亚戈
关键词	李群 无穷小生成元 偏微分方程 科学计算软件
其他题名	The application of Lie group to the solution of several classical partial differential equations
中文摘要	Today, energy plays a very important role in the development and civilization of the social. On the other hand, studying and developing the clear energy is the only way we should to do. Ocean energy is one kind of new and renewable energy, and is being studied in many countries. The research of the nonlinear partial differential equations (PDEs) is the basis of the conversion of wave energy. In the methods of solving the PDEs, Lie’s theory is applicable to construct the transformation between the dependent and independent variables, and the symmetry group allows us to reduce the order of the equation, and gives us a rule that we can gain the transformation. In this thesis, we introduce the methods of solving the PDEs numerically, and point out the disadvantage and the limitation firstly. In chapter 2, beginning with the basic knowledge of groups, we introduce the classical symmetries, non-classical symmetries, generalized symmetries, approximate symmetries and direct methods. In chapter 3, the heat equations are calculated firstly by classical and non-classical symmetries, through the constant of characteristic equation given special values, we gained the determining equations and infinitesimal invariance, so we can get the solutions by replace the original equation and calculate the reduce equation . And then the Burgers equations, Boussinesq equations, KdV equations are considered to access their rich solutions. The significance of this thesis is that the scientific analysis software is employed in the symbolic computation at the same time the Lie group symmetry is applied in the solution to the PDEs, which improves the applicability of the Lie group theory and increases the abundance solutions of several classical PDEs. The works provide some useful idea in the solution to the PDEs in hydrodynamics, accumulate some theory foundation for the basis research of wave energy, and give some useful help for the practical design in the ocean emerging. Key words: Lie Group, infinitesimal generator, partial differential equations (PDEs), scientific analysis software.
语种	中文
公开日期	2011-07-10 ; 2011-07-15
页码	58
内容类型	学位论文
源URL	[http://ir.giec.ac.cn/handle/344007/4047]
专题	中国科学院广州能源研究所
推荐引用方式 GB/T 7714	何再明. 李群方法在求解几类偏微分方程中的应用, The application of Lie group to the solution of several classical partial differential equations[D]. 广州能源研究所. 中国科学院广州能源研究所. 2006.

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