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首页> 外文期刊>Siberian Mathematical Journal >A PROPERTY OF THE DEFINING EQUATIONS FOR THE LIE ALGEBRA IN THE GROUP CLASSIFICATION PROBLEM FOR WAVE EQUATIONS
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A PROPERTY OF THE DEFINING EQUATIONS FOR THE LIE ALGEBRA IN THE GROUP CLASSIFICATION PROBLEM FOR WAVE EQUATIONS

机译:波动方程组分类问题中李代数定义方程的性质

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摘要

We solve the group classification problem for nonlinear hyperbolic systems of differential equations. The admissible continuous group of transformations has the Lie algebra of dimension less than 5. This main statement follows from the principal property of the defining equations of the admissible Lie algebra: the commutator of two solutions is a solution. Using equivalence transformations we classify nonlinear systems in accordance with the well-known Lie algebra structures of dimension 3 and 4.
机译:我们解决了非线性双曲型微分方程组的组分类问题。可容许的连续变换组的维数小于5的李代数。该主要说明是基于可允许李代数的定义方程式的主要性质得出的:两个解的交换子是一个解。使用等价变换,我们根据维度3和4的著名李代数结构对非线性系统进行分类。

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