The Painlev property for a (2+1)-dimensional Korteweg–de Vries (KdV) extension, the combined KP3 (Kadomtsev–Petviashvili) and KP4 (cKP3-4), is proved by using Kruskal’s simplification. The truncated Painlev expansion is used to find the Schwartz form, the Bcklund/Levi transformations, and the residual nonlocal symmetry. The residual symmetry is localized to find its finite Bcklund transformation. The local point symmetries of the model constitute a centerless Kac–Moody–Virasoro algebra. The local point symmetries are used to find the related group-invariant reductions including a new Lax integrable model with a fourth-order spectral problem. The finite transformation theorem or the Lie point symmetry group is obtained by using a direct method.

(2+1) 维 Korteweg-de Vries (KdV) 扩展的 Painlev 属性，组合 KP3 (Kadomtsev-Petviashvili) 和 KP4 (cKP3-4)，通过使用 Kruskal 的简化证明。截断的 Painlev 展开式用于查找 Schwartz 形式、Bcklund/Levi 变换和残余非局部对称性。残余对称性被局部化以找到其有限的 Bcklund 变换。模型的局部点对称性构成了无心 Kac-Moody-Virasoro 代数。局部点对称性用于找到相关的组不变约简，包括具有四阶谱问题的新 Lax 可积模型。有限变换定理或李点对称群是用直接法得到的。