JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2019, Vol. 54 ›› Issue (2): 111-120.doi: 10.6040/j.issn.1671-9352.0.2017.565

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Exact solution of GKP equation with variable coefficients

YANG Fei, LIU Xi-qiang*   

  1. School of Mathematics Science, Liaocheng University, Liaocheng 252059, Shandong, China
  • Published:2019-02-25

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Abstract: In order to solve a kind of GKP equation with variable coefficients, the form of the solution is first constructed then combined with the new solutions of different auxiliary equations and corresponding Bäcklund transformations. With the help of mathematical calculation software, the new exact solutions of infinite sequence soliton-like of the equation are obtained. The types of these solutions include Jacobi elliptic function type, trigonometric function type, exponential function type, hyperbolic function type, etc. Using the hypothetical solitary wave method, this kind of GKP equation with variable coefficients is studied. Then alternative solitary wave solutions are obtained.

Key words: GKP equation with variable coefficients, auxiliary equation, Bä, cklund transformation, infinite sequence exact solutions

CLC Number: 

  • O175.2
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