Invariance of Painlevé property for some reduced (1+1)-dimensional equations

doi:10.1088/1674-1056/22/11/110203

Abstract We study the Painlevé property of the (1+1)-dimensional equations arising from the symmetry reduction for the (2+1)-dimensional ones. Firstly, we derive the similarity reduction of the (2+1)-dimensional potential Calogero–Bogoyavlenskii–Schiff (CBS) equation and Konopelchenko–Dubrovsky (KD) equations with the optimal system of the admitted one-dimensional subalgebras. Secondly, by analyzing the reduced CBS, KD, and Burgers equations with Painlevé test, respectively, we find both the Painlevé integrability, and the number and location of resonance points are invariant, if the similarity variables include all of the independent variables.

Keywords: similarity reduction Painlevé analysis resonance point (1+1)-dimensional reduced equation

Received: 09 December 2012
Revised: 28 May 2013
Accepted manuscript online:

PACS:	02.30.Sv
	02.30.Ik	(Integrable systems)
	02.30.Jr	(Partial differential equations)

Fund: Project supported by the Natural Science Foundation of Shandong Province, China (Grant Nos. ZR2011AQ017 and ZR2010AM028) and the Fundamental Research Funds for the Central Universities of Ministry of Education of China (Grant No. 13CX02010A).

Corresponding Authors: Zhi Hong-Yan
E-mail: zhihongyan@126.com

Cite this article:

Zhi Hong-Yan (智红燕), Chang Hui (常辉) Invariance of Painlevé property for some reduced (1+1)-dimensional equations 2013 Chin. Phys. B 22 110203

[1]	Ablowitz M J, Ramani A and Segur H 1978 Lett. Nuovo. Cimento 23 333
[2]	Ablowitz M J and Segur H 1981 Solitons and the Inverse Scattering Transform (Philadelphia: Society for Industrial and Applied Mathematics)
[3]	Tang X Y and Lou S Y 2001 Chin. Phys. 10 897
[4]	Zhang Y F and Zhang H Q 2002 Chin. Phys. 11 319
[5]	Xie S Y and Lin J 2010 Chin. Phys. B 19 050201
[6]	Bogoyavlenskii O I 1990 Math. USSR-Izv. 34 245
[7]	Schiff J 1992 NATO ASI Ser. B 278 393
[8]	Toda K and Yu S J 2000 J. Math. Phys. 41 4747
[9]	Zhang H P, Chen Y and Li B 2009 Acta Phys. Sin. 58 7393 (in Chinese)
[10]	Bruzon M, Gandarias M L, Muriel C, Ramirez J, Saez A and Romero F R 2003 Theor. Math. Phys. 137 1367
[11]	Gandarias M and Bruzon M 2008 79th Annual Meeting of the International Association of Applied Mathematics and Mechanics, May 28, 2008, Bremen, Germany p. 10591
[12]	Gandarias M and Bruzon M 2008 American Conference on Applied Mathematics (math’08), March 24-26, Harvard, Massachusetts, USA, p. 153
[13]	Wazwaz A M 2008 Appl. Math. Comput. 196 363
[14]	Wazwaz A M 2008 Appl. Math. Comput. 203 592
[15]	Ayati Z and Biazar J 2009 Iran. J. Optim. 1 173
[16]	Ruan H Y 2002 J. Phys. Soc. Jpn. 71 453
[17]	Chen Y, Li B and Zhang H Q 2003 Commun. Theor. Phys. 40 137
[18]	Wang J M and Yang X 2012 Nonlinear Anal. 75 2256
[19]	Yan Z Y and Zhang H Q 2002 Comput. Math. Appl. 44 1439
[20]	Cui K 2012 Chin. Phys. Lett. 29 060508
[21]	Lu Z S, Duan L X and Xie F D 2010 Chin. Phys. Lett. 27 070502
[22]	Ivanova N M, Sophocleous C and Tracina R 2012 Z. Angew. Math. Phys. 61 793
[23]	Konopelchenko B G and Dubrovsky V G 1984 Phys. Lett. A 102 15
[24]	Xu P B, Gao Y T, Yu X, Wang L and Lin G D 2011 Commun. Theor. Phys. 55 1017
[25]	Zhi H Y 2008 Appl. Math. Comput. 203 931
[26]	Weiss J, Tabor M and Carnevale G 1983 J. Math. Phys. 24 522
[27]	Olver P J 1986 Application of Lie Group to Differential Equations (Berlin: Springer)
[28]	Bluman G and Kumei S 1989 Symmetries and Differential Equations (New York: Springer)

[1]	Effect of bio-tissue deformation behavior due to intratumoral injection on magnetic hyperthermia Yundong Tang(汤云东), Jian Zou(邹建), Rodolfo C.C. Flesch, and Tao Jin(金涛). Chin. Phys. B, 2023, 32(3): 034304.
[2]	Acoustic propagation uncertainty in internal wave environments using an ocean-acoustic joint model Fei Gao(高飞), Fanghua Xu(徐芳华), Zhenglin Li(李整林), Jixing Qin(秦继兴), and Qinya Zhang(章沁雅). Chin. Phys. B, 2023, 32(3): 034302.
[3]	Performance analysis of quantum key distribution using polarized coherent-states in free-space channel Zengte Zheng(郑增特), Ziyang Chen(陈子扬), Luyu Huang(黄露雨),Xiangyu Wang(王翔宇), and Song Yu(喻松). Chin. Phys. B, 2023, 32(3): 030306.
[4]	Quantitative analysis of soliton interactions based on the exact solutions of the nonlinear Schrödinger equation Xuefeng Zhang(张雪峰), Tao Xu(许韬), Min Li(李敏), and Yue Meng(孟悦). Chin. Phys. B, 2023, 32(1): 010505.
[5]	A novel algorithm to analyze the dynamics of digital chaotic maps in finite-precision domain Chunlei Fan(范春雷) and Qun Ding(丁群). Chin. Phys. B, 2023, 32(1): 010501.
[6]	Computational studies on magnetism and ferroelectricity Ke Xu(徐可), Junsheng Feng(冯俊生), and Hongjun Xiang(向红军). Chin. Phys. B, 2022, 31(9): 097505.
[7]	Finite-key analysis of practical time-bin high-dimensional quantum key distribution with afterpulse effect Yu Zhou(周雨), Chun Zhou(周淳), Yang Wang(汪洋), Yi-Fei Lu(陆宜飞), Mu-Sheng Jiang(江木生), Xiao-Xu Zhang(张晓旭), and Wan-Su Bao(鲍皖苏). Chin. Phys. B, 2022, 31(8): 080303.
[8]	Bifurcation analysis of visual angle model with anticipated time and stabilizing driving behavior Xueyi Guan(管学义), Rongjun Cheng(程荣军), and Hongxia Ge(葛红霞). Chin. Phys. B, 2022, 31(7): 070507.
[9]	A nonlinear wave coupling algorithm and its programing and application in plasma turbulences Yong Shen(沈勇), Yu-Hang Shen(沈煜航), Jia-Qi Dong(董家齐), Kai-Jun Zhao(赵开君), Zhong-Bing Shi(石中兵), and Ji-Quan Li(李继全). Chin. Phys. B, 2022, 31(6): 065206.
[10]	Influences of Marangoni convection and variable magnetic field on hybrid nanofluid thin-film flow past a stretching surface Noor Wali Khan, Arshad Khan, Muhammad Usman, Taza Gul, Abir Mouldi, and Ameni Brahmia. Chin. Phys. B, 2022, 31(6): 064403.
[11]	Effect of the target positions on the rapid identification of aluminum alloys by using filament-induced breakdown spectroscopy combined with machine learning Xiaoguang Li(李晓光), Xuetong Lu(陆雪童), Yong Zhang(张勇),Shaozhong Song(宋少忠), Zuoqiang Hao(郝作强), and Xun Gao(高勋). Chin. Phys. B, 2022, 31(5): 054212.
[12]	Fringe removal algorithms for atomic absorption images: A survey Gaoyi Lei(雷高益), Chencheng Tang(唐陈成), and Yueyang Zhai(翟跃阳). Chin. Phys. B, 2022, 31(5): 050313.
[13]	Maximum entropy mobility spectrum analysis for the type-I Weyl semimetal TaAs Wen-Chong Li(李文充), Ling-Xiao Zhao(赵凌霄), Hai-Jun Zhao(赵海军),Gen-Fu Chen(陈根富), and Zhi-Xiang Shi(施智祥). Chin. Phys. B, 2022, 31(5): 057103.
[14]	A quantitative analysis method for contact force of mechanism with a clearance joint based on entropy weight and its application in a six-bar mechanism Zhen-Nan Chen(陈镇男), Meng-Bo Qian(钱孟波), Fu-Xing Sun(孙福兴), and Jia-Xuan Pan(潘佳煊). Chin. Phys. B, 2022, 31(4): 044501.
[15]	Numerical simulation of two droplets impacting upon a dynamic liquid film Quan-Yuan Zeng(曾全元), Xiao-Hua Zhang(张小华), and Dao-Bin Ji(纪道斌). Chin. Phys. B, 2022, 31(4): 046801.

No Suggested Reading articles found!

Viewed

Full text

Abstract

Cited

Metrics
Related Articles

Invariance of Painlevé property for some reduced (1+1)-dimensional equations

Cite this article:

Online attention