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

作　　者：Xiao-Bo Wang Man Jia Sen-Yue Lou 王晓波;贾曼;楼森岳(School of Physical Science and Technology,Ningbo University,Ningbo 315211,China)

机构地区：[1]School of Physical Science and Technology,Ningbo University,Ningbo 315211,China

出　　处：《Chinese Physics B》2021年第1期178-184,共7页中国物理B（英文版）

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

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 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.

关 键 词：Painlevéproperty residual symmetry Schwartz form Bäcklund transforms D’Alembert waves symmetry reductions Kac–Moody–Virasoro algebra (2+1)-dimensional KdV equation 

分 类 号：O175[理学—数学]