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Application of Generalized Logistic Function to Travelling Wave Solutions for a Class of Nonlinear Evolution Equations

Author

Listed:
  • Lingxiao Li

    (School of Mathematics & Statistics, Henan University of Science & Technology, Luoyang 471000, China)

  • Mingliang Wang

    (School of Mathematics & Statistics, Lanzhou University, Lanzhou 730000, China)

  • Jinliang Zhang

    (School of Mathematics & Statistics, Henan University of Science & Technology, Luoyang 471000, China)

Abstract

The generalized Logistic function that solves a first-order nonlinear ODE with an arbitrary positive power term of the dependent variable is introduced in this paper, by means of which the traveling wave solutions of a class of nonlinear evolution equations, including the generalized Fisher equation, the generalized Nagumo equation, the generalized Burgers-Fisher equation, the generalized Gardner equation, the generalized KdV-Burgers equation, and the generalized Benney equation, are obtained successfully. In these particular cases, traveling wave solutions of several important model PDEs in mathematical physics are also discovered.

Suggested Citation

  • Lingxiao Li & Mingliang Wang & Jinliang Zhang, 2022. "Application of Generalized Logistic Function to Travelling Wave Solutions for a Class of Nonlinear Evolution Equations," Mathematics, MDPI, vol. 10(21), pages 1-13, October.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:21:p:4017-:d:957061
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    References listed on IDEAS

    as
    1. He, Ji-Huan & Wu, Xu-Hong, 2006. "Exp-function method for nonlinear wave equations," Chaos, Solitons & Fractals, Elsevier, vol. 30(3), pages 700-708.
    2. Yusufoğlu, Elcin & Bekir, Ahmet, 2008. "Exact solutions of coupled nonlinear evolution equations," Chaos, Solitons & Fractals, Elsevier, vol. 37(3), pages 842-848.
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