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Chin. Phys. B, 2013, Vol. 22(11): 110203    DOI: 10.1088/1674-1056/22/11/110203
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Invariance of Painlevé property for some reduced (1+1)-dimensional equations

Zhi Hong-Yan (智红燕)a, Chang Hui (常辉)b
a College of Science, China University of Petroleum, Qingdao 266580, China;
b College of science, Qingdao Binhai University, Qingdao 266510, China
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

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