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Chin. Phys. B, 2018, Vol. 27(4): 040202    DOI: 10.1088/1674-1056/27/4/040202
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Integrability classification and exact solutions to generalized variable-coefficient nonlinear evolution equation

Han-Ze Liu(刘汉泽), Li-Xiang Zhang(张丽香)
School of Mathematical Sciences, Liaocheng University, Liaocheng 252059, China
Abstract  This paper is concerned with the generalized variable-coefficient nonlinear evolution equation (vc-NLEE). The complete integrability classification is presented, and the integrable conditions for the generalized variable-coefficient equations are obtained by the Painlevé analysis. Then, the exact explicit solutions to these vc-NLEEs are investigated by the truncated expansion method, and the Lax pairs (LP) of the vc-NLEEs are constructed in terms of the integrable conditions.
Keywords:  Painlevé test      integrability classification      Lax pair      truncated expansion      exact solution  
Received:  01 December 2017      Revised:  01 January 2018      Published:  05 April 2018
PACS:  02.30.Jr (Partial differential equations)  
  02.30.Ik (Integrable systems)  
Fund: Project supported by the National Natural Science Foundation of China (Grant No. 11171041) and the High-Level Personnel Foundation of Liaocheng University (Grant No. 31805).
Corresponding Authors:  Han-Ze Liu     E-mail:  bzliuhanze@163.com

Cite this article: 

Han-Ze Liu(刘汉泽), Li-Xiang Zhang(张丽香) Integrability classification and exact solutions to generalized variable-coefficient nonlinear evolution equation 2018 Chin. Phys. B 27 040202

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