The generalized Kudryashov method to obtain exact traveling wave solutions of the PHI-four equation and the Fisher equation

Abstract

In recent years, searching exact traveling wave solutions to nonlinear evolution equations (NLEEs) has become a remarkable topic of research. In this article, we obtain exact traveling wave solutions of two significant NLEEs, namely, the PHI-four equation and the Fisher equation involving parameters by using the generalized Kudryashov method. We attain some exponential type solutions including kink soliton, bisymmetry soliton, and periodic solution when the parameters receive different values. We provide the graphical representations of the respective solutions also.