In this article, similarity reductions of the (2 $+$ 1)‐dimensional Bogoyavlenskii‐Schieff equation of higher order have been done by Lie group method. We have determine the geometric vector field, infinitesimal generators, symmetric groups, and commutator table of Lie algebra with the help of Lie symmetry analysis. The new close form solutions and similarity solutions of the (2 $+$ 1)‐dimensional Bogoyavlenskii‐Schieff equation of higher order have been determined from the reduction equations. Also, the conservation laws have been derived by invoking the new conservation theorem proposed by Ibragimov.

中文翻译：

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等离子体物理中的Lie对称性分析，具有精确解的对称性约简以及（2 + 1）维Bogoyavlenskii-Schieff方程的守恒律

在本文中，（2 $+$1）-维高等Bogoyavlenskii-Schieff方程是通过李群方法完成的。我们借助李对称性分析，确定了李代数的几何矢量场，无穷小生成器，对称群和换向表。（2）新的闭式解和相似解$+$1）-维数高的Bogoyavlenskii-Schieff方程已由约化方程确定。同样，通过调用伊布拉吉莫夫提出的新的守恒定理，得出了守恒定律。