In this paper, the classical Lie group method is employed to obtain exact solutions for a nonlinear partial differential equation (NLPDE) derived from the reduced quasi-classical self-dual Yang–Mills equation. An infinite-dimensional Lie algebra is obtained, and by utilizing a seven-dimensional subspace of this algebra, the commutator table and adjoint representation table are constructed. These tables facilitate the construction of the optimal system for the equation, leading to precise solutions. The obtained solutions are presented graphically, accompanied by a suitable analysis.

中文翻译：

---

简化准经典自对偶 Yang-Mills 方程的李对称分析、最优系统和 NLPDE 精确解

本文采用经典李群方法来获得由简化准经典自对偶杨-米尔斯方程导出的非线性偏微分方程（NLPDE）的精确解。得到无限维李代数，并利用该代数的七维子空间构造交换子表和伴随表示表。这些表格有助于构建方程的最佳系统，从而获得精确的解。获得的解决方案以图形方式呈现，并附有适当的分析。