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

• 来源期刊: 中国物理B（英文版）
• 年，卷（期）: 2021,（1）
• 页码范围: 200-207
• 页数: 8页
• 语种: 英文
• DOI: 10.1088/1674-1056/abaeda

摘要

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. The truncated Painlevé expansion is used to find the Schwartz form, the B?cklund/Levi transformations, and the residual nonlocal symmetry. The residual symmetry is localized to find its finite B?cklund 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.