New Exact Traveling Wave Solution of Fisher Kolmogorov-Petrovskii-Piskunov Equation for Favorite Genes Spreading by -expansion Method

Subject Areas : Journal of Chemical Health Risks

Mohammad Gholami baladezaei ¹ , Morteza Gachpazan ² , Saedeh Foadian ³ , Hossein Mohammad-Pour Kargar ⁴

1 - Department of Applied Mathematics, School of Mathematical Sciences, Ferdowsi University of Mashhad, Mashhad, Iran
2 - Department of Applied Mathematics, School of Mathematical Sciences, Ferdowsi University of Mashhad, Mashhad, Iran
3 - Department of Applied Mathematics, Islamic Azad University, Damghan Branch, Damghan, Iran
4 - Department of Biology, Islamic Azad University, Damghan Branch, Damghan, Iran

Received: 2021-01-08 Accepted : 2021-07-12 Published : 2022-09-01

Keywords: Fisher KPP equation, Traveling wave solutions, Partial differential equation (PDE), expansion method, 2020 MSC: 35Q92, 35C05, 35C10,

Abstract :

Although designing and developing a mathematical model is extremely important in the mathematics but finding solution for designing model is essential as well. Thus one cannot propose a model without offering its solutions. In the mathematical modeling, there are many models based on nonlinear partial differential equations. In such models, there is no general method for solving any problem. However, numerical methods, approximate methods or analytical methods are available for some problems. It is clear that among the methods for solving a model based on partial differential equations, analytical methods are preferred, but for all problems, it is not possible to provide an exact solution. In this case, some methods can provide a class of solutions. In such methods, techniques that lead to more solutions are more important, but the use of different methods can provide a wide class of solutions. For this reason, various methods are used to find the possible solution of nonlinear partial differential equations. One of these methods is the expansion method. Since one of the well-known equations with wide application in genetics and gene mutation is the Fisher Kolmogorov-Petrovskii-Piskunov (Fisher KPP) equation, we applied expansion method, for finding exact traveling wave solutions which are based on the solutions of Bernoulli ordinary differential equation.

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