| 群理论解非线性KdV方程的探讨 |
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| 引用本文： | 李银.群理论解非线性KdV方程的探讨[J].韶关学院学报,2010,31(6). |
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| 作者姓名： | 李银 |
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| 作者单位： | 韶关学院数学与信息科学学院,广东,韶关512005 |
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| 基金项目： | 国家自然科学基金项目，韶关学院项目基金 |
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| 摘 要： | 基于单参数变换群(OPG)的基本理论,通过构造群不变量和对称方法作为函数变换的基础,讨论了非线性方程在变换群作用下的不变性,以经典的KdV方程为例,给出了使偏微分方程形式不变的变换群,从而得到化简或求解.
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| 关 键 词： | 李群理论 单参数变换群 偏微分方程 |
The group theory of nonlinear equation |
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| LI Yin.The group theory of nonlinear equation[J].Journal of Shaoguan University(Social Science Edition),2010,31(6). |
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| Authors: | LI Yin |
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| Institution: | LI Yin (College of Mathematics and Information Sciences,Shaoguan University,Shaoguan 512005,Guangdong,China) |
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| Abstract: | Based on one-parameter transformation group (OPG) of the basic theory, we discuss the invariance in the transformation group invariance under the given equation by constructing a group of non-ariable and symmetric methods as the basis of function transformation. And we take the classical KdV equation as example so that we obtain the transformation group, simplification or solution of partial differential equations. |
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| Keywords: | Lie group theory one-parameter transformation group partial differential equations |
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