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

Lingxiao Li (), Mingliang Wang and Jinliang Zhang
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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

Mathematics, 2022, vol. 10, issue 21, 1-13

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.

Keywords: generalized Logistic function; traveling wave solution; generalized Fisher equation; generalized Nagumo equation; generalized Burgers-Fisher equation; generalized Gardner equation; generalized KdV-Burgers equation; generalized Benney equation (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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