Abstract
Considered under their standard form, the fifth-order KdV equations are a sort of reading table on which new prototypes of higher order solitary waves residing there, have been uncovered and revealed to broad daylight. The mathematical tool that made it possible to explore and analyze this equation is the Bogning-Djeumen Tchaho-Kofané method extended to the new implicit Bogning' functions. The analytical form of the solutions chosen in this manuscript is particular in the sense that it contains within its bosom, a package of solitary waves made up of three solitons, especially, the bright type soliton, the hybrid soliton and the dark type soliton which we estimate capable in their interactions of generating new hybrid or multi-form solitons. Existence conditions of the obtained solitons have been determined. It emerges that, these existence conditions of the chosen ansatz could open the way to other new varieties of fifth-order KdV equations including to which it will be one of the solutions. Some of the obtained solitons are exact solutions. Intense numerical simulations highlighted numerical stability and confirmed the hybrid character of the obtained solutions. These results will help to model new nonlinear wave phenomena, in plasma media and in fluid dynamics, especially, on the shallow water surface.
Highlights
Many natural phenomena regularly occur in the universe
The second sub-section, for its part, is working on an intense numerical simulation in order to reassure itself of the stability of the obtained solutions with a view to a probable future application and for a possible confirmation of the hybrid characters (planned when choosing of the ansatz given by Equation (18) below) of these obtained solutions
We can say with enthusiasm that, the application of the Bogning-Djeumen Tchaho-Kofané method (BDKm) extended to implicit Bogning’ (iB)-functions, to the standard form of the fifth-order KdV equations, has enabled to reveal new prototypes of solitary waves of higher order, which are for some, approximate hybrid solutions, and for others, exact solutions of this equation
Summary
Many natural phenomena regularly occur in the universe. These phenomena can in certain cases be destructive for the environment in which they take place. A lot of work remains to be done because many other phenomena at the origin of the new predictable or unpredictable behaviors of these different systems still have to be detected, understood and explained in order to guarantee all of humanity a future safely In this manuscript, One tracks down, using the Bogning-Djeumen Tchaho-Kofané method (BDKm) extended to the new implicit Bogning’ (iB) functions, new prototypes of solitary waves of the standard KdV equation while revealing the hybrid character of these waves.
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