Applied Mathematics and Mechanics

, Volume 26, Issue 1, pp 101–107 | Cite as

Explicit solutions to the coupled KdV equations with variable coefficients

  • Xu Gui-qiong
  • Li Zhi-bin


By means of sn-function expansion method and cn-function expansion method, several kinds of explicit solutions to the coupled KdV equations with variable coefficients are obtained, which include three sets of periodic wave-like solutions. These solutions degenerate to solitary wave-like solutions at a certain limit. Some new solutions are presented.

Key words

en-function method sn-function method periodic wave-like solution solitary wave-like solution coupled KdV equations with variable coefficient 

Chinese Library Classification


2000 Mathematics Subject Classification

74G05 35Q51 35Q53 


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  1. [1]
    Hereman W, Banerjee P P, Korpel A. Exact solitary wave solutions of nonlinear evolution and wave equations using a direct algebraic method[J].J. Phys. A, Math Gen, 1986,19(3): 607–628.MATHMathSciNetCrossRefGoogle Scholar
  2. [2]
    Parkes E J, Duffy B R. The Jacobi elliptic function method for finding periodic-wave solutions to nonlinear evolution equations[J].Phys. Lett A, 2002,295(6): 280–286.MATHMathSciNetCrossRefGoogle Scholar
  3. [3]
    Hu Xingbiao, Wang Daoliu, Qian Xiannin. Soliton solutions and symmetries of the 2+1 dimensional Kaup-Kupershmidt equation[J].Phys Lett A, 1999,262(6): 409–415.MathSciNetCrossRefGoogle Scholar
  4. [4]
    Fan Engui, Zhang Hongqing. A note on the homogeneous balance method[J].Phys Lett A, 1998,246(5): 403–406.CrossRefGoogle Scholar
  5. [5]
    Wang Mingliang. Solitary wave solutions for variant Boussinesq equations[J].Phys Lett A, 1995,199(3): 169–172.MathSciNetCrossRefGoogle Scholar
  6. [6]
    Fu Zuntao, Liu Shikuo, Liu Shida,et al., New Jacobi elliptic function expansion and new periodic solutions of nonlinear wave equations[J].Phys Lett A, 2001,290(2): 72–76.MathSciNetCrossRefGoogle Scholar
  7. [7]
    Xu Guiqiong, Li Zhibin. Mixing exponential method and its application to the solitary wave solution of the nonlinear evolution equation[J].Acta Phys Sin, 2002,51(5): 946–950. (in Chinese)Google Scholar
  8. [8]
    Wen Shuangchun, Xu Wencheng, Guo Qi,et al. The solition evolution to the variable coefficient nonlinear Schrödinger equation[J].Sci China A, 1997,27(10): 949–953. (in Chinese)Google Scholar
  9. [9]
    Ruan Hangyu, Chen Yixin. New method for explicit solution of the variable coefficient nonlinear evolution equation[J].Acta Phys Sin, 2000,49(2): 177–180. (in Chinese)Google Scholar
  10. [10]
    Yan Zhenya, Zhang Hongqing. Similarity reductions for 2+1 dimensional variable coefficient generalized Kadotsev-Petviashvili equation[J].Applied Mathematics and Mechanics (English Edition), 2000,21(6): 645–650.MathSciNetGoogle Scholar
  11. [11]
    Zhang Jiefang, Chen Fangyue. Truncated expansion method and the new solutions to the generalized KdV equation[J].Acta Phys Sin, 2001,50(9): 1648–1656. (in Chinese)Google Scholar
  12. [12]
    Zhang Jinliang Hu Xiaomin, Wang Mingliang. Backlünd transformation and solitary wave solutions with variable velocity to coupled KdV equations with variable coefficient[J].J Hangzhou Institute of Electronic Engineering, 2002,22,(1): 59–61. (in Chinese)Google Scholar
  13. [13]
    Liu Shikuo, Fu Zuntao, Liu Shida,et al. Jacobi elliptic function expansion solution to the variable coefficient nonlinear equations[J].Acta Phys Sin, 2002,51(9): 1923–1926. (in Chinese)Google Scholar

Copyright information

© Editorial Committee of Applied Mathematics and Mechanics 2005

Authors and Affiliations

  • Xu Gui-qiong
    • 1
  • Li Zhi-bin
    • 2
  1. 1.Department of Information AdministrationShanghai UniversityShanghaiPR China
  2. 2.Department of Computer ScienceEast China Normal UniversityShanghaiPR China

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