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

Yu-Ming Chu,Dumitru Baleanu,Sidra Riaz,Hadi Rezazadeh,Shumaila Javeed,Zengtao Chen

doi:10.1155/2020/5098329

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.

Highlights

The nonlinearity in the world prevails thoroughly; it is significant to develop nonlinear models including partial differential equations [1,2,3,4]
Nonlinear conformable partial differential equations (PDEs) attracted the interest of many researchers because of their vast applications in different fields, for example, in chemistry, acoustic, fluid dynamics, image processing, biology, physics, vibration, and control [5,6,7]
Different effective and reliable techniques are proposed like the homotopy analysis method [13], homotopy perturbation technique [14], extended hyperbolic tangent method [15, 16], hyperbolic function method [17], subequation method [18], and exponential rational function method [19] to get solutions

Summary

Introduction

The nonlinearity in the world prevails thoroughly; it is significant to develop nonlinear models including partial differential equations [1,2,3,4]. FIM can only be applied to integrable PDEs. The focus of this paper is to find the exact solutions of conformable biological models. The focus of this paper is to find the exact solutions of conformable biological models It includes KPP and its Advances in Mathematical Physics derived models, namely, FHN and NW. An effective technique named as FIM was adopted to acquire the exact solutions of KPP, FHN, and NW equations. The work is novel as the exact solutions of considered models using FIM are not presented before in the literature. Conformable derivative is described in Section 2; the proposed technique FIM is discussed in Section 3; the solutions of conformable KPP, FHN, and NW equations are presented, and Section 5 contains summary and further recommendations Conformable derivative is described in Section 2; the proposed technique FIM is discussed in Section 3; the solutions of conformable KPP, FHN, and NW equations are presented in Section 4, and Section 5 contains summary and further recommendations

Derivative

Methodology

Implementation of FIM

Conclusion

Conflicts of Interest