Painlevé property, local and nonlocal symmetries and symmetry reductions for a (2+1)-dimensional integrable KdV equation
arXiv:2007.02296 · doi:10.1088/1674-1056/abb304
Abstract
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 Bäcklund/Levi transformations and the residual nonlocal symmetry. The residual symmetry is localized to find its finite Bäcklund 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.
arXiv comment9 pages
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