Author(s)

Clovis Taki Djeumen Tchaho^1,2*, Hugues Martial Omanda^1,3, Gaston N’tchayi Mbourou⁴, Jean Roger Bogning⁵, Timoléon Crépin Kofané^6,7

¹African Centre for Advanced Studies, Yaoundé, Cameroon.
²Lycée Technique Fulbert Bongotha, Moanda, Gabon.
³Laboratoire Pluridisciplinaire des Sciences, Ecole Normale Supérieure, Libreville, Gabon.
⁴Laboratoire de Mécanique des Matériaux, Ecole Polytechnique, Université des Sciences et Techniques de Masuku, Franceville, Gabon.
⁵Department of Physics, Higher Teacher Training College, University of Bamenda, Bamenda, Cameroon.
⁶Department of Physics, Faculty of Science, University of Yaoundé I, Yaoundé, Cameroon.
⁷Centre d'Excellence Africain en Technologie de l'Information et de la Télécommunication, University of Yaoundé I, Yaoundé, Cameroon.

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.

Standard KdV Equations, Bogning-Djeumen Tchaho-Kofané Method, Higher Order Solitary Wave, Multi-Form Solitons, New Implicit Bogning’ Functions

Tchaho, C. , Omanda, H. , Mbourou, G. , Bogning, J. and Kofané, T. (2021) Higher Order Solitary Wave Solutions of the Standard KdV Equations. Open Journal of Applied Sciences, 11, 103-125. doi: 10.4236/ojapps.2021.111008.