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

doi:10.1088/1674-1056/010501

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 B\"acklund/Levi transformations, and the residual nonlocal symmetry. The residual symmetry is localized to find its finite B\"acklund 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.

Keywords: Painlevé property residual symmetry Schwartz form B\"acklund transforms D'Alembert waves symmetry reductions Kac-Moody-Virasoro algebra (2+1)-dimensional KdV equation

Revised: 30 July 2020
Accepted manuscript online:

PACS:	05.45.Yv	(Solitons)
	02.30.Ik	(Integrable systems)
	47.20.Ky	(Nonlinearity, bifurcation, and symmetry breaking)
	52.35.Mw	(Nonlinear phenomena: waves, wave propagation, and other interactions (including parametric effects, mode coupling, ponderomotive effects, etc.))

Fund: Project supported by the National Natural Science Foundation of China (Grant Nos. 11975131 and 11435005) and the K C Wong Magna Fund in Ningbo University.\vglue2pt

Corresponding Authors: ^†Corresponding author. E-mail: lousenyue@nbu.edu.cn

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Xiao-Bo Wang(王晓波), Man Jia(贾曼), and Sen-Yue Lou(楼森岳) Painlevé property, local and nonlocal symmetries, and symmetry reductions for a (2+1)-dimensional integrable KdV equation 2021 Chin. Phys. B 30 010501

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

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