JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2019, Vol. 54 ›› Issue (12): 24-31.doi: 10.6040/j.issn.1671-9352.0.2018.513

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Solving explicit new travelling wave solutions of KdV-Burgers-Kuramoto equation by Riccati equation

LIN Fu-biao, ZHANG Qian-hong   

  1. School of Mathematics and Statistics, Guizhou University of Finance and Economics, Guiyang 550025, Guizhou, China
  • Published:2019-12-11

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Abstract: Firstly, 8 types explicit new analytical solutions of the Riccati equation are presented by the trial function method combing with the related properties of solutions for the Riccati equation. Secondly, the reduced equations and invariant solutions of KdV-Burgers-Kuramoto(KBK)equation are given by the Lie group analysis method. Finally, the extended tanh-function method and 8 types explicit new analytical solutions of the Riccati equation are used to solve the reduced equation of KBK equation, moreover, many types explicit new travelling wave solutions of KBK equation are found. In addition, periodic types, rational types of exponential function and trigonometric function of explicit new travelling wave solutions of other similar nonlinear partial differential equations can be obtained by use of the extended tanh-function method, 8 types explicit new analytical solutions of the Riccati equation and the Lie group analysis method.

Key words: Riccati equation, KdV-Burgers-Kuramoto equation, Lie group analysis method, extended tanh-function method, travelling wave solution

CLC Number: 

  • O175.29
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