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非线性离散的Klein-Gordon方程的对称约化Symmetries of the Discrete Nonlinear Klein-Gordon Eq-uation
潘阳, 张丽华, 李德生, 潘树丰
Klein-Gordon方程, 相似变换, 不变解 Klein-Gordon Equation; Similarity Transformation; Invariant Solution
《Advances in Applied Mathematics》, Vol.2 No.4, 2013-11-29
本文把离散的Lie点对称群分析方法应用于非线性离散的Klein-Gordon方程。由于该方程不易应用李点对称进行约化，所以本文首先引入一个相似变换将其转化为易被李点对称约化的新方程，然后用李点对称方法约化新方程得到其不变解，最后再通过相似变换得到原非线性离散的Klein-Gordon方程的解。>In this paper, the discrete Lie point symmetry group analysis method is applied on the discrete nonlinear Klein-Gordon equation. Since this equation is not easy to be reduced by Lie point symmetry method, firstly, this paper introduces a similarity transformation to change this equation into a new equation which can be reduced easily by Lie point symmetry method. Then the new equation is reduced by Lie point symmetry method and its invariant solutions are obtained. Finally, the solutions of the primal discrete nonlinear Klein- Gordon equation are acquired by the similarity transformation again.