In the present work, abundant group-invariant solutions of (\(2+1\))-dimensional Bogoyavlenskii–Schieff equation have been investigated using Lie symmetry analysis. The Lie infinitesimal generators, all the geometric vector fields, their commutative and adjoint relations are provided by utilising the Lie symmetry method. The Lie symmetry method depends on the invariance criteria of Lie groups, which results in the reduction of independent variables by one. A repeated process of Lie symmetry reductions, using the double, triple and septuple combinations between the considered vectors, converts the Bogoyavlenskii–Schieff (BS) equation into nonlinear ordinary differential equations (ODEs) which furnish numerous explicit exact solutions with the help of computerised symbolic computation. The obtained group-invariant solutions are entirely new and distinct from the earlier established findings. As far as possible, a comparison of our reported results with the previous findings is given. The dynamical behaviour of solutions is discussed both analytically as well as graphically via their evolutionary wave profiles by considering suitable choices of arbitrary constants and functions. To ensure rich physical structures, the exact closed-form solutions are supplemented via numerical simulation, which produce some bright solitons, doubly solitons, parabolic waves, U-shaped solitons and asymptotic nature.

在目前的工作中，（\（2 + 1 \））维Bogoyavlenskii–Schieff方程已使用李对称分析进行了研究。利用李对称性方法，提供了李无穷小生成器，所有几何矢量场，它们的可交换关系和伴随关系。李对称性方法取决于李群的不变性标准，这导致自变量减少一。利用考虑的向量之间的双重，三次和七种组合，重复进行李氏对称性降低的过程，将Bogoyavlenskii–Schieff（BS）方程转换为非线性常微分方程（ODE），借助计算机符号化可以提供大量的显式精确解。计算。所获得的组不变解是全新的，并且与先前确定的发现不同。越远越好，将我们报告的结果与以前的发现进行了比较。解的动力学行为通过考虑任意常数和功能的合适的选择通过两个其进化波轮廓分析以及图形地讨论的。为了确保丰富的物理结构，通过数值模拟补充了精确的闭式解，从而生成了一些明亮的孤子，双孤子，抛物线波，U形孤子和渐近性质。