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Chin. Phys. B, 2013, Vol. 22(5): 050203    DOI: 10.1088/1674-1056/22/5/050203
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Painlevé integrability of generalized fifth-order KdV equation with variable coefficients: Exact solutions and their interactions

Xu Gui-Qiong
Department of Information Management, College of Management, Shanghai University, Shanghai 200444, China
Abstract  By means of singularity structure analysis, the integrability of a generalized fifth-order KdV equation is investigated. It is proven that this equation passes the Painlevé test for integrability only for three distinct cases. Moreover, the multi-soliton solutions are presented for this equation under three sets of integrable conditions. Finally, by selecting appropriate parameters, we analyze the evolution of two solitons, which is especially interesting as it may describe the overtaking and the head-on collisions of solitary waves of different shapes and different types.
Keywords:  generalized fifth-order KdV equation      Painlevé      integrability      soliton solution      symbolic computation  
Received:  21 November 2012      Revised:  05 January 2013      Published:  01 April 2013
PACS:  02.30.Ik (Integrable systems)  
  05.45.Yv (Solitons)  
  02.30.Jr (Partial differential equations)  
Fund: Projects supported by the National Natural Science Foundation of China (Grant Nos. 11201290 and 71103118).
Corresponding Authors:  Xu Gui-Qiong     E-mail:

Cite this article: 

Xu Gui-Qiong Painlevé integrability of generalized fifth-order KdV equation with variable coefficients: Exact solutions and their interactions 2013 Chin. Phys. B 22 050203

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