主要考虑非线性波方程组的一些简单对称及其构成的李代数，并利用所得对称给出该方程组的一些单参数变换群。
In this paper, the symmetries and Lie algebra of a coupled nonlinear wave equation were discussed. One-parameter transformation groups of this equation were obtained by using the symmetries.
通过力学分析，建立了离心调速器系统的动力学方程，应用李雅普·诺夫直接方法得到该系统稳定平衡点的条件。
By using mechanical analysis, the dynamic equation of the system was established, the Lyapunov direct method was applied to obtain stability conditions of system equilibrium points.
首先，提出了求解一般动力学方程的李级数方法，并给出具体实施办法，它是泰勒展开方法的一个推广。
Firstly, Lie series method to solve general nonlinear dynamic system is presented, and the implementation method is given in detail. It is an expansion of the Talor series method.
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