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.

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。

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The general time-dependent SchrOdinger equation with external perturbance needs to be resolved through Lie group decompositions.

而一般具有外加微扰作用力的含时薛定谔方程的求解需要通过李群分解。

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It is shown that for some relatively simple conditions, exact analytical solutions of the non linear consolidation equation can be obtained by using the approach of the transformation of Lie group.

研究表明，对于一些相对简单的边界条件，通过李群变换的方法可以得到非线性固结方程的完整解析解。

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