Kink-Bright Solitary Wave Solutions of the Generalized Kuramoto-Sivashinsky Equation

The quintessence of this work articulates around the construction of the solitary wave solutions of the generalized Kuramoto-Sivashinsky equation presenting a generalized non-linearity term instead of the usual Burger’s non-linearity, by the means of the Bogning-Djeumen Tchaho-Kofané method, extended to the implicit Bogning’ functions. We focus our attention on the case where the parameter which generalizes this non-linearity takes the value two. The innovation, at least on the analytical form of the solution proposed here, comes from the fact that it is a package of waves in which the two main bright and kink solitons coexist, respectively. When the values of the parameters of the solution and those of the system are suitably chosen, this cohabitation can be the seat of many types of solitons. So the solutions we are looking for are the combinations of kink and bright called: kink-bright solitary waves. To be reassured of the observable and applicable characters of the solutions obtained within the framework of this work, an intense numerical simulation has been performed which confirmed a stability in a relatively long time, and at the same time revealed some geometric properties between certain obtained solutions. These solutions will help to understand and explain so many phenomena that occur in the chemical turbulence process.