Overall, rational fractions are considered. Based on these rational fractions, we have generalized the new explicit Djeumen Tchaho formulas of decomposition. It looms up that these formulas facilitate the decomposition of rational fractions whatever be the degrees of numerator and of denominator. This generalization made it possible to establish a new principle of summation. We have successfully applied this generalization to several rational fractions chosen arbitrarily. Certain new β-hyperbolic functions proposed from these formulas in previous works have made it possible to construct new b-solitary wave solutions of the generalized Fisher equation. The different profiles displayed by the obtained graphical representations made it possible to confirm their solitary wave characters.

explicit Djeumen Tchaho formulas, b-solitary wave solutions, generalized Fisher equation, solitary wave characters, new principle of summation

Received: July 7, 2024; Revised: August 19, 2024; Accepted: September 26, 2024; Published: November 14, 2024

How to cite this article: Clovis Taki Djeumen Tchaho, Generalization of the explicit Djeumen Tchaho formulas of decomposition and new exact b-solitary wave solutions for the generalized Fisher equation, Far East Journal of Dynamical Systems 37(2) (2024), 233-263. https://doi.org/10.17654/0972111824010

This Open Access Article is Licensed under Creative Commons Attribution 4.0 International License

References:
[1] X. Hubaut, Méthode de Horner-Mathématique du secondaire, Université Libre de Bruxelles, 1995-2000. https//xavier.hubaut.info/coursmath/.
[2] N. Roby, Lois polynomes et lois formelles en théorie des modules, Ann. Scient. Éc. Norn. Sup. 3e série, t. 80 (1963), 213-348.
[3] Méthode de Ruffini-Horner 2008. https//fr.m.wikipedia.org.
[4] Méthode de Horner: définition et explications, 2008.
https//www.techno.science.net.
[5] C. T. Djeumen Tchaho, Explicit formulas for the derivatives and decompositions by the polynomial coefficients and extension to hyperbolic functions as new solution prototypes for KdV equation, Far East J. Dyn. Syst. 37(1) (2024), 13-49.
[6] C. T. Djeumen Tchaho, Explicit Djeumen Tchaho formulas and new beta-hyperbolic functions as solutions of some nonlinear evolution equations, Far East J. Dyn. Syst. 37(2) (2024), 107-135.
[7] V. M. Kenkre and M. N. Kuperman, Applicability of the Fisher equation to bacterial population dynamics, Phys. Rev. E 67 (2003), 051921.
[8] H. Triki and A.-M. Wazwaz, On the soliton dynamics of the generalized Fisher equation with time-dependent coefficients, Romanian Reports in Physics 68 (2016), 65-78.
[9] S. Fedotov, Nonuniform reaction rate distribution for the generalized Fisher equation: ignition ahead of the reaction front, Phys. Rev. E 60 (1999), 4958.
[10] G. Abramson, A. R. Bishop and V. M. Kenkre, Effects of transport memory and nonlinear damping in a generalized Fisher’s equation, Phys. Rev. E 64 (2001), 066615.
[11] Arzu Öğün and Cevat Kart, Exact solutions of Fisher and generalized Fisher equations with variable coefficients, Acta Math. Appl. Sin. 23 (2007), 563.
[12] X. Y. Wang, Exact and explicit solitary wave solutions for the generalized Fisher equation, Phys. Lett. A 131 (1988), 277.
[13] A. M. Wazwaz, Travelling wave solutions of generalized forms of Burgers, Burgers-KdV and Burgers-Huxley equations, Appl. Math. Comput. 169 (2005), 639.
[14] H. Zhang and D. Lu, Exact solutions of the variable coefficient Burgers-Fisher equation with forced term, Int. J. Nonlinear Sci. 9 (2010), 252.