Higher Order Solitary Wave Solutions of the Standard KdV Equations
| Autor: | Jean Roger Bogning, Gaston N. 'tchayi Mbourou, Hugues Martial Omanda, Clovis Taki Djeumen Tchaho, Timoleon Crepin Kofane |
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| Rok vydání: | 2021 |
| Předmět: |
Surface (mathematics)
Physics 050210 logistics & transportation 05 social sciences Mathematical analysis 02 engineering and technology Type (model theory) 021001 nanoscience & nanotechnology Nonlinear system Nonlinear Sciences::Exactly Solvable and Integrable Systems 0502 economics and business Fluid dynamics Soliton 0210 nano-technology Korteweg–de Vries equation Nonlinear Sciences::Pattern Formation and Solitons Numerical stability Ansatz |
| Zdroj: | Open Journal of Applied Sciences. 11:103-125 |
| ISSN: | 2165-3925 2165-3917 |
| DOI: | 10.4236/ojapps.2021.111008 |
| Popis: | 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-Kofane 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. |
| Databáze: | OpenAIRE |
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