In this article, we construct exact solutions of the Bogoyavlenskii equation using $(1/G^{\prime })$-expansion and $(G^{\prime }/G,1/G)$-expansion techniques. Both techniques have been successfully implemented to obtain exact solutions including hyperbolic, complex trigonometric, trigonometric and rational solutions of the Bogoyavlenskii equation. 3D, contour and 2D graphics are presented of the solutions obtained for different special values. Further, the advantages and disadvantages of both the techniques have been discussed in this study. The proposed techniques are reliable and applicable for attaining wave solutions of nonlinear differential equations. Also, these techniques can greatly minimize the size of computing work compared to other available techniques.

在本文中，我们使用以下公式构造Bogoyavlenskii方程的精确解 $（\mathrm{1个}/G^{\prime }）$-扩展和 $（G^{\prime }/G，\mathrm{1个}/G）$扩展技术。两种技术均已成功实现，以获得精确的解，包括Bogoyavlenskii方程的双曲型，复三角函数，三角函数和有理解。给出了针对不同特殊值获得的解决方案的3D，轮廓和2D图形。此外，在这项研究中已经讨论了这两种技术的优缺点。所提出的技术是可靠的并且可用于获得非线性微分方程的波动解。而且，与其他可用技术相比，这些技术可以极大地减小计算工作的规模。