Applied Mathematics and Mechanics

, Volume 9, Issue 3, pp 311–316 | Cite as

Solitary wave and similarity solutions of the combined KdV equation

  • Pan Xiu-de


In this paper, we discuss a property of solitary wave solutions of the combined KdV equation. Meantime, we point out that the combined KdV equation can be reduced to the Painlevé equation. Furthermore, utilizing special transformations of similarity variables, we derive a kind of new partial differential equations.


Solitary Wave Wave Solution Similarity Solution Solitary Wave Solution Progressive Wave 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    Toda, M., Progr. Theor. Phys. Suppl.,45 (1970) 174.Google Scholar
  2. [2]
    Dai Shi-qiang, Solitary waves at the interface of a two-layer fluid,Applied Mathematics and Mechanics,3, 6 (1982).Google Scholar
  3. [3]
    Wadati Miki, Wave propagation in nonlinear lattices, I. II.,J. P. S. 38, 3 Japan (1975), 673–686.CrossRefGoogle Scholar
  4. [4]
    Ablowitz, M.J. and H. Segur,Phys. Rev. Lett.,38, (1977), 1103.MathSciNetCrossRefGoogle Scholar
  5. [5]
    Wang Ming-liang,J. Lanzhou Univ.,19, (1983), 9–18.Google Scholar
  6. [6]
    Bluman, G. W. and J.D. Cole,Similarity Methods for Differential Equation Springer, Berlin (1974).Google Scholar

Copyright information

© SUT 1988

Authors and Affiliations

  • Pan Xiu-de
    • 1
  1. 1.Zheijing UniversityHangzhou

Personalised recommendations