The unified group classification method for the generalized nonlinear wave equation and its partial difference schemes
The unified group classification method for the generalized nonlinear wave equation and its partial difference schemes
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DOI：
10.1016/j.amc.2014.11.017
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发表时间：
2015-01
期刊：
影响因子：
--
通讯作者：
Hanze Liu
中科院分区：
文献类型：
--
作者：
Hanze Liu
本文分别研究了具有不同格的广义非线性二阶方程和离散二阶方程。采用统一对称分析方法，对方程进行了完全群分类。在点对称意义下，得到了连续非线性方程的所有向量场。作为它的特例，给出了其他一些重要的非线性方程的向量场。然后，我们发展了处理偏差分格式的统一群分类方法（P Δ S），给出了关于给定任意解析函数f (u)的所有差分格式的点对称性。
This paper is concerned with the generalized nonlinear second-order equation and its discrete counterpart furnished with different lattices, respectively. By the unified symmetry analysis method, the complete group classifications of the equations are performed. In the sense of point symmetry, all of the vector fields of the continuous nonlinear equation are obtained. As its special cases, the vector fields of some other important nonlinear equations are provided. Then, we develop the unified group classification method for dealing with partial difference schemes (P Δ S), all of the point symmetries of the difference schemes are presented with respect to the given arbitrary analytic function f (u).