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

• Editors’ suggestions • 上一篇下一篇

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-.

参考文献

1 Lou S Y 1056/ab9699 2020 Chin. Phys. B 29 080502 DOI: http://dx.doi.org/10.1088/1674-
2 Crighton D G1995 Appl. Math. 39 39
3 Kadomtsev B B and Petviashvili V I1970 Sov. Phys. Dokl. 15 539
4 Nizhnik L P1980 Sov. Phys. Dokl. 25 706
5 Veselov A P and Novikov S P1984 Sov. Math. Dokl. 30 588
6 Novikov S P and Veselov A P 2789(86)90187- 9 1986 Physica D 18 267 DOI: http://dx.doi.org/10.1016/0167-
7 Lou S Y and Hu X B 1997 J. Math. Phys. 38 6401 DOI: http://dx.doi.org/10.1063/1.532219
8 Lou S Y and Ruan H Y 4470/35/2/310 2001 J. Phys. A: Math. Gen. 35 305 DOI: http://dx.doi.org/10.1088/0305-
9 Boiti M, Leon J J P, Manna M and Pempinelli F 5611/2/3/005 1986 Inverse Problems 2 271 DOI: http://dx.doi.org/10.1088/0266-
10 Ito M 1990 J. Phys. Soc. Jpn. 49 771 DOI: http://dx.doi.org/10.1143/JPSJ.49.771
11 Lou S Y 6528/ab833e 2020 J. Phys. Commun. 4 041002 DOI: http://dx.doi.org/10.1088/2399-
12 Xu D H and Lou S Y 2020 Acta Phys. Sin. 69 014208 (in Chinese) DOI: http://dx.doi.org/10.7498/aps.69.20191347
13 Yan Z W and Lou S Y 2020 Appl. Math. Lett. 104 106271 DOI: http://dx.doi.org/10.1016/j.aml.2020.106271
14 Weiss J, Tabor M and Carnevale G 1983 J. Math. Phys. 24 522 DOI: http://dx.doi.org/10.1063/1.525721
15 Conte R 9601(89)90072- 8 1989 Phys. Lett. A 140 383 DOI: http://dx.doi.org/10.1016/0375-
16 Lou S Y 1998- 0523 1998 Z. Naturforsch A 53 251 DOI: http://dx.doi.org/10.1515/zna-
17 Gao X N, Lou S Y and Tang X Y2013 J. High Energy Phys. 5 029
18 Li Y Q, Chen J C, Chen Y and Lou S Y 307X/31/1/010201 2014 Chin. Phys. Lett. 31 010201 DOI: http://dx.doi.org/10.1088/0256-
19 Liu S J, Tang X Y and Lou S Y 1056/27/6/060201 2018 Chin. Phys. B 27 060201 DOI: http://dx.doi.org/10.1088/1674-
20 Lou S Y, Hu X R and Chen Y 8113/45/15/155209 2012 J. Phys. A: Math. Theor. 45 155209 DOI: http://dx.doi.org/10.1088/1751-
21 Cheng X P, Chen C L and Lou S Y 2014 Wave Motion 51 1298 DOI: http://dx.doi.org/10.1016/j.wavemoti.2014.07.012
22 Lou S Y 1993 Phys. Rev. Lett. 71 4099 DOI: http://dx.doi.org/10.1103/PhysRevLett.71.4099
23 Lou S Y 4470/26/17/043 1993 J. Phys. A: Math. Gen. 26 4387 DOI: http://dx.doi.org/10.1088/0305-
24 David D, Kamran N, Levi D and Winternitz P 1986 J. Math. Phys. 27 1225 DOI: http://dx.doi.org/10.1063/1.527129
25 Lou S Y, Rogers C and Schief W K 2003 J. Math. Phys. 44 5869 DOI: http://dx.doi.org/10.1063/1.1625077
26 Lou S Y and Tang X Y 2004 J. Math. Phys. 45 1020 DOI: http://dx.doi.org/10.1063/1.1645651
27 Lou S Y and Ma H C2005 J. Phys.A: Math. Gen. 38 L129
28 Lou S Y and Ma H C 2006 Chaos, Solitons and Fractals 30 804 DOI: http://dx.doi.org/10.1016/j.chaos.2005.04.090

Metrics

Viewed

Full text

144

HTML			PDF

最新录用	在线预览	正式出版	最新录用	在线预览	正式出版
0	0	0	0	0	144

来源	本网站	其他网站

次数	141	3
比例	98%	2%

Abstract

591

最新录用	在线预览	正式出版

0	0	591

	来源	本网站

	次数	591
	比例	100%

Cited

Web of Science	Crossref	ScienceDirect	Search for Citations in Google Scholar >>


This page requires you have already subscribed to WoS.

Shared

[1]	Shubin Wang(王树斌), Xin Zhang(张鑫), Guoli Ma(马国利), and Daiyin Zhu(朱岱寅). All-optical switches based on three-soliton inelastic interaction and its application in optical communication systems[J]. 中国物理B, 2023, 32(3): 30506-030506.
[2]	Yiyuan Zhang(张艺源), Ziqi Liu(刘子琪), Jiaxin Qi(齐家馨), and Hongli An(安红利). Soliton molecules, T-breather molecules and some interaction solutions in the (2+1)-dimensional generalized KDKK equation[J]. 中国物理B, 2023, 32(3): 30505-030505.
[3]	Wei Qi(漆伟), Xiao-Gang Guo(郭晓刚), Liang-Wei Dong(董亮伟), and Xiao-Fei Zhang(张晓斐). Modulational instability of a resonantly polariton condensate in discrete lattices[J]. 中国物理B, 2023, 32(3): 30502-030502.
[4]	Wen-Xiu Ma(马文秀). Matrix integrable fifth-order mKdV equations and their soliton solutions[J]. 中国物理B, 2023, 32(2): 20201-020201.
[5]	Nkeh Oma Nfor, Patrick Guemkam Ghomsi, and Francois Marie Moukam Kakmeni. Localized nonlinear waves in a myelinated nerve fiber with self-excitable membrane[J]. 中国物理B, 2023, 32(2): 20504-020504.
[6]	D Chevizovich, S Zdravković, A V Chizhov, and Z Ivić. Charge self-trapping in two strand biomolecules: Adiabatic polaron approach[J]. 中国物理B, 2023, 32(1): 10506-010506.
[7]	Xuefeng Zhang(张雪峰), Tao Xu(许韬), Min Li(李敏), and Yue Meng(孟悦). Quantitative analysis of soliton interactions based on the exact solutions of the nonlinear Schrödinger equation[J]. 中国物理B, 2023, 32(1): 10505-010505.
[8]	Jing Wang(王静), Hua Wu(吴华), and Da-Jun Zhang(张大军). Reciprocal transformations of the space-time shifted nonlocal short pulse equations[J]. 中国物理B, 2022, 31(12): 120201-120201.
[9]	Guofei Zhang(张国飞), Jingsong He(贺劲松), and Yi Cheng(程艺). Riemann-Hilbert approach and N double-pole solutions for a nonlinear Schrödinger-type equation[J]. 中国物理B, 2022, 31(11): 110201-110201.
[10]	Jing Wang(王静), Xue-Li Ding(丁学利), and Biao Li(李彪). Fusionable and fissionable waves of (2+1)-dimensional shallow water wave equation[J]. 中国物理B, 2022, 31(10): 100502-100502.
[11]	Shu-Wen Guan(关淑文), Ling-Zheng Meng(孟令正), and Li-Chen Zhao(赵立臣). Oscillation properties of matter-wave bright solitons in harmonic potentials[J]. 中国物理B, 2022, 31(8): 80506-080506.
[12]	Denghui Li(李登慧), Fei Wang(王菲), and Zhaowen Yan(颜昭雯). Quantum fields presentation and generating functions of symplectic Schur functions and symplectic universal characters[J]. 中国物理B, 2022, 31(8): 80202-080202.
[13]	Hong-Cai Ma(马红彩), Yi-Dan Gao(高一丹), and Ai-Ping Deng(邓爱平). Solutions of novel soliton molecules and their interactions of (2 + 1)-dimensional potential Boiti-Leon-Manna-Pempinelli equation[J]. 中国物理B, 2022, 31(7): 70201-070201.
[14]	Ahmet Bekir and Emad H M Zahran. Nonlinear dynamical wave structures of Zoomeron equation for population models[J]. 中国物理B, 2022, 31(6): 60401-060401.
[15]	Xi-zhong Liu(刘希忠) and Jun Yu(俞军). A nonlocal Boussinesq equation: Multiple-soliton solutions and symmetry analysis[J]. 中国物理B, 2022, 31(5): 50201-050201.

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

PDF (PC)

赞

可视化

摘要/Abstract

引用本文

使用本文

参考文献

相关文章 15

Metrics

本文评价

推荐阅读 0