Acta mathematica scientia,Series A ›› 2019, Vol. 39 ›› Issue (3): 451-460.

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The Integrability of the KdV-Shallow Water Waves Equation

Xiaohong Hao1(),Zhilong Cheng2,*()   

  1. 1 Wenzheng College of Soochow University, Jiangsu Suzhou 215104
    2 School of Mathematics and Physics, Suzhou University of Sience and Technology, Jiangsu Suzhou 215009
  • Received:2017-04-10 Online:2019-06-26 Published:2019-06-27
  • Contact: Zhilong Cheng;
  • Supported by:
    the Natural Science Foundation of Anhui Province(KJ2016A071)


In this paper, the binary Bell polynomials to construct bilinear forma, bilinear Bäcklund transformation, Lax pair of the KdV-shallow water waves equation. Through bilinear Bäcklund transformation, some soliton solutions are presented. Moreover, the infinite conservation laws are also derived by Bell polynomials, all conserved densities and fluxes are given with explicit recursion formulas.

Key words: Bäcklund transformation, Lax pair, Infinite conservation laws

CLC Number: 

  • O175.24