Journal of South China University of Technology(Natural Science Edition) ›› 2012, Vol. 40 ›› Issue (10): 96-101.doi: 1000-565X(2012)10-0096-06

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New Singular Solutions of KdV and mKdV Equations

Liu Zheng-rong  Tang Hao   

  1. Department of Mathematics,South China University of Technology,Guangzhou 510640,Guangdong,China
  • Received:2012-07-10 Online:2012-10-25 Published:2012-09-01
  • Contact: Liu Zheng-rong ( born in 1955) ，male，professor，Ph．D．tutor，mainly reasearches on nonlinear dynamic systems． E-mail:liuzhr@ scut.edu.cn
  • About author:Liu Zheng-rong ( born in 1955) ，male，professor，Ph．D．tutor，mainly reasearches on nonlinear dynamic systems．
  • Supported by:

    Supported by the National Natural Science Foundation of China ( 11171115)

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Abstract:

This paper deals with the singular solutions of the famous KdV and mKdV equations. In the investigation,first,the corresponding planar systems of these equations are established. Then,through some special orbits of the corresponding planar systems,some new singular solutions of these equations are obtained. Finally,by employing the singular solutions of the mKdV equation and the Miura transformations,other singular solutions of the KdV equation are presented.

Key words: KdV equation, mKdV equation, singular solution, Miura transformation