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Chin. Phys. B, 2011, Vol. 20(12): 120202    DOI: 10.1088/1674-1056/20/12/120202
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Traveling wave solutions for two nonlinear evolution equations with nonlinear terms of any order

Feng Qing-Hua(冯青华)a)b), Meng Fan-Wei(孟凡伟)b), and Zhang Yao-Ming(张耀明)a)
a School of Science, Shandong University of Technology, Zibo 255049, China; School of Mathematical Sciences, Qufu Normal University, Qufu 273165, China
Abstract  In this paper, based on the known first integral method and the Riccati sub-ordinary differential equation (ODE) method, we try to seek the exact solutions of the general Gardner equation and the general Benjamin-Bona-Mahoney equation. As a result, some traveling wave solutions for the two nonlinear equations are established successfully. Also we make a comparison between the two methods. It turns out that the Riccati sub-ODE method is more effective than the first integral method in handling the proposed problems, and more general solutions are constructed by the Riccati sub-ODE method.
Keywords:  first integral method      Riccati equation      nonlinear equation      traveling wave solution  
Received:  01 April 2011      Revised:  22 June 2011      Accepted manuscript online: 
PACS:  02.30.Jr (Partial differential equations)  
  04.20.Jb (Exact solutions)  
Fund: Project supported by the National Natural Science Foundation of China (Grant No. 10571110), the Natural Science Foundation of Shandong Province of China (Grant Nos. ZR2009AM011 and ZR2010AZ003), and the Specialized Research Fund for the Doctoral Program of Higher Education of China (Grant No. 20103705110003).

Cite this article: 

Feng Qing-Hua(冯青华), Meng Fan-Wei(孟凡伟), and Zhang Yao-Ming(张耀明) Traveling wave solutions for two nonlinear evolution equations with nonlinear terms of any order 2011 Chin. Phys. B 20 120202

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