The new explicit Djeumen Tchaho formulas as well as new beta-hyperbolic functions are presented. First, the formulas relating to the decomposition by the polynomial coefficients are used to decompose some types of rational fractions. Then, the new formulas relating to derivative calculations are used for successfully deriving some rational fractions previously put in decomposed form as well as some beta-hyperbolic functions. Secondly, some new functions presented are used to construct new solitary wave solutions of beta-hyperbolic types. It appears that these new formulas are simple and easy to use while, the influence of the nonlinearity coefficient on the formation of some obtained undulatory structures is observed. To judge the particle stability and observability of the new obtained solutions, numerical simulations are performed. These one revealed the stable spatiotemporal evolutions of these solutions, from that moment on corroborating the analytical predictions with a good accuracy.

explicit Djeumen Tchaho formulas, beta-hyperbolic functions, nonlinear evolution equations, polynomial coefficients, Euclidean division theorem

Received: March 21, 2024; Accepted: May 10, 2024; Published: June 20, 2024

How to cite this article: Clovis Taki Djeumen Tchaho, Explicit Djeumen Tchaho formulas and new beta-hyperbolic functions as solutions of some nonlinear evolution equations, Far East Journal of Dynamical Systems 37(2) (2024), 107-135. https://doi.org/10.17654/0972111824006

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

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