Hybridization of Solitary Wave Solutions in (2+1)-dimentional Complex Ginzburg-Landau Equation

Abstract

The reflection carried out in this manuscript concerns the construction of prototypes of hybrid solitary waves, solutions of the (2+1)-dimensional complex Ginzburg-Landau equation. The principle of construction consists in injecting into the equation to be solved an ansatz that one would like solution, and that its analytical sequence results from a combination of the analytical sequences of the classical solitary waves. Then, the constraints imposed by the resolution allow to extract exact or approximate solution. As part of this work, the solution function to be constructed from the start is made up of a combination of four analytical sequences of solitary waves of the kink and pulse type. To this end, we have obtained, using a rigorous mathematical approach, important results whose graphic exploitations have made it possible to better characterize them.