Abstract
•A Fractal model of Complex Ginzburg-Landau Equation (CGL) is proposed.•Complex Ginzburg-Landau Equation (CGL) with three forms of nonlinearity Soliton solutions are obtained by means of a principle of variation.•The novel requirements for solitons are calculated.•This equation is an important fractal model for oscillating phenomena and optical fibers.
The complex Ginzburg-Landau Equation (CGLE) is one of the non-trivial models for addressing the dynamics of oscillating, highly nonlinear processes right before the start of oscillations. This paper presents the complex Ginzburg-Landau fractal model with three types of nonlinearity. The variational approach provides soliton solutions for the CGLE in terms of Kerr, parabolic, and quadratic laws of nonlinearity. New bright and dark soliton solutions for the CGLE are developed. The necessary novel conditions that guarantee the existence of suitable solitary waves are introduced. Monitoring solutions 3D and 2D plots are illustrated by choosing a range of appropriate values of parameters.