Painlevé property, local and nonlocal symmetries, and symmetry reductions for a (2+1)-dimensional integrable KdV equation*

The Painlevé 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. truncated expansion used to find Schwartz form, Bäcklund/Levi transformations, residual nonlocal symmetry. symmetry localized its finite Bäcklund transformation. local point symmetries of model constitute centerless Kac–Moody–Virasoro algebra. are related group-invariant reductions including new Lax integrable with fourth-order spectral problem. transformation theorem or Lie group obtained direct method.