中国物理B ›› 2013, Vol. 22 ›› Issue (11): 110203-110203.doi: 10.1088/1674-1056/22/11/110203

• GENERAL • 上一篇    下一篇

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

智红燕a, 常辉b   

  1. a College of Science, China University of Petroleum, Qingdao 266580, China;
    b College of science, Qingdao Binhai University, Qingdao 266510, China
  • 收稿日期:2012-12-09 修回日期:2013-05-28 出版日期:2013-09-28 发布日期:2013-09-28
  • 基金资助:
    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).

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

Zhi Hong-Yan (智红燕)a, Chang Hui (常辉)b   

  1. a College of Science, China University of Petroleum, Qingdao 266580, China;
    b College of science, Qingdao Binhai University, Qingdao 266510, China
  • Received:2012-12-09 Revised:2013-05-28 Online:2013-09-28 Published:2013-09-28
  • Contact: Zhi Hong-Yan E-mail:zhihongyan@126.com
  • Supported by:
    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).

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摘要： 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.

关键词: similarity reduction, Painlevé, analysis, resonance point, (1+1)-dimensional reduced equation

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.

Key words: similarity reduction, Painlevé, analysis, resonance point, (1+1)-dimensional reduced equation

中图分类号: 

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