TITLE:
Construction of New Surface Wave Solutions of the Modified KdV Equation
AUTHORS:
Clovis Taki Djeumen Tchaho, Jean Pierre Ngantcha, Thierry Blanchard Ekogo, Bruno Rodin Mbock Um, Hugues Martial Omanda, Hugues Martial Omanda, Jean Roger Bogning
KEYWORDS:
Surface Hybrid Waves, Modified Korteweg-De Vries Equation, Bogning-Djeumen Tchaho-Kofané Method, Hybrid Prototypes, Multi-Form Structures
JOURNAL NAME:
Open Journal of Applied Sciences,
Vol.12 No.2,
February
21,
2022
ABSTRACT: The major concern of this work is to propose new prototypes of surface
hybrid waves, in particular waves propagating without sprawl or deformation on
the surface of a fluid. The model considered for this purpose is the modified
KdV (Korteweg-de Vries) equation. A peculiarity of the obtained solutions is
that they form packages constituted by combinations of waves belonging to the two main families of well-known
bright and dark solitary waves. This putting together creates
competitions between the different components of the considered packages which,
following the values assigned to the parameters of the considered system and in
relation to those of the wave parameters, generate hybrid or multi-form
structures. The direct method of resolution which made possible the obtained
results is that of Bogning-Djeumen Tchaho-Kofane extended to the new implicit
Bogning functions. The existence conditions of some solutions are obtained. The
numerical simulations carried out with a view to testing the observable and
applicable characters of the obtained solutions revealed their stabilities over
a relatively long time, and at the same time, confirmed the recommended
theoretical forecasts. We are convinced that the solutions proposed as part of
this work will make it possible to detect, understand and explain some physical
phenomena linked to fluid molecular interactions, former or new, which
constantly occur on the fluid surfaces, mainly at the shallow water surface.