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

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References:

1. El-Hachem M., McCue S.W., Jin W., Du Y., Simpson M.J., 2019. Revisiting the Fisher-Kolmogorov-Petrovsky-Piskunov equation to interpret the spreading-extinction dichotomy. Proc Math Phys Eng Sci. 475(2229), 0378.

2. Loewe L., 2008. Genetic Mutation, Nature Education 1(1), 113.

3. Fisher R.A., 1937. The wave of advance of advantageous genes. Ann Eugen. 7, 355– 369.

4. Bacaer N., 2011. A Short History of Mathematical Population Dynamics, Springer-Verlag.

5. Kolmogorov A., Petrovskii I., Piskunov N., 1937. Study of a Diffusion Equation That Is Related to the Growth of a Quality of Matter and Its Application to a Biological Problem. Moscow University Mathematics Bulletin. 1, 1-26.

 6. Adomian G., 1995. Fisher-Kolmogorov equation. Appl Math Lett. 8(2), 51-52.

 7. Zheng B., 2011. A new Bernoulli Sub-ODE method for constructing traveling wave solutions for two nonlinear equations with any order, U.P.B.Sci. Bull A. 73(3), 85-94.

8. Kudryashov N.A., Zakharchenko A.S., 2014. A note on solutions of the generalized Fisher equation. Applied Mathematics Letters. 32, 53-56.

9. Malfliet W., Hereman W., 1996. The Tanh method: Exact solutions of nonlinear evolution and wave equations. Physica Scripta. 54, 563-568.

10. Tashin Khan A., Naher H., 2018. Solitons and periodic solutions of the Fisher equation with nonlinear ordinary differential equation as auxiliary equation. American Journal of Applied Mathematics and Statistics. 6(6), 244-252.

11. Taha W.M., Noorani M.S.M., 2014. Application of the -expansion method for the generalized Fisher’s equation and modified equal width equation. Journal of the Association of Arab Universities for Basic and Applied Sciences. 15, 82–89.

12. Zayed E.M.E., Amer Y.A., 2015. Exact solutions for the nonlinear KPP equation by using the Riccati equation method combined with the -expansion method. Scientific Research and Essays. 10(3), 86-96.

13. Yokus A., 2011. Solutions of some nonlinear partial differential equations and comparison of their solutions, Ph.D. Thesis, Firat Uni- versity, Elazig.

14. Zheng B., 2012. Application of a generalized Bernoulli Sub-ODE method for finding traveling solution of some nonlinear equations, Wseas Transactions on Mathematics. 11(7), 618-626.

15. Macías-Díaza J.E., Medina-Ramírezb I., A.Puric A., 2009. Numerical treatment of the spherically symmetric solutions of a generalized Fisher–Kolmogorov–Petrovsky–Piscounovequation. Journal of Computational and Applied Mathematics. 231, 851–868.

16. Unal A.O., 2013. On the Kolmogorov-Petrovskii-Piskunov equation. Commun Fac Sci Univ Ank Series A1. 62(1), 1-10.

17. Loyinmi A.C., Akinfe T.K., 2020. Exact solutions to the family of Fisher’s reaction-diffusion equation using Elzaki homotopy transformation perturbation method. Engineering Reports. 2, 1-32.