New Exact Solutions of Kolmogorov Petrovskii Piskunov Equation, Fitzhugh Nagumo Equation, and Newell-Whitehead Equation

Abstract

This work presents the new exact solutions of nonlinear partial differential equations (PDEs). The solutions are acquired by using an effectual approach, the first integral method (FIM). The suggested technique is implemented to obtain the solutions of space-time Kolmogorov Petrovskii Piskunov (KPP) equation and its derived equations, namely, Fitzhugh Nagumo (FHN) equation and Newell-Whitehead (NW) equation. The considered models are significant in biology. The KPP equation describes genetic model for spread of dominant gene through population. The FHN equation is imperative in the study of intercellular trigger waves. Similarly, the NW equation is applied for chemical reactions, Faraday instability, and Rayleigh-Benard convection. The proposed technique FIM can be applied to find the exact solutions of PDEs.