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

doi:10.1088/1674-1056/010501

中国物理B ›› 2021, Vol. 30 ›› Issue (1): 10501-.doi: 10.1088/1674-1056/010501

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修回日期:2020-07-30 出版日期:2020-12-17 发布日期:2020-12-23

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

Xiao-Bo Wang(王晓波), Man Jia(贾曼), and Sen-Yue Lou(楼森岳)

School of Physical Science and Technology, Ningbo University, Ningbo\/ 315211, China

Revised:2020-07-30 Online:2020-12-17 Published:2020-12-23
Contact: ^†Corresponding author. E-mail: lousenyue@nbu.edu.cn
Supported by:
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

摘要/Abstract

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.

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

中图分类号: (Solitons)

05.45.Yv

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.))

. [J]. 中国物理B, 2021, 30(1): 10501-.

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[J]. Chin. Phys. B, 2021, 30(1): 10501-.

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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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