A study of variation in dynamical behavior of fractional complex Ginzburg-Landau model for different fractional operators

Abstract

The fractional complex Ginzburg–Landau model is widely used in the description of wave propagation through optical transmission lines. It has many useful applications in the fields of telecommunications and nonlinear optics. This paper investigates the fractional effects of the complex Ginzburg–Landau model with quadratic–cubic, anti–cubic and generalized anti–cubic laws of nonlinearity by using generalized projective Riccati equation method. The variation in the traveling wave behavior of the governing model is examined for beta, conformable and M-truncated derivatives. Some constraint conditions are carried out during mathematical analysis, which are further used for evaluating the traveling wave solutions. The analytic solutions of the considered model are determined in terms of hyperbolic and trigonometric function solutions. Consequently, dark, bright, kink, bell-shaped and singular solitons are extracted. The reported solutions are presented using 2D and 3D graphs. These graphs are showing the fractional effects for different values of fractional parameter. The evolution of the wave profiles shows that the retrieved solitons become similar for all three definitions of fractional derivatives as the fractional parameter approaches unity.

Keywords

• Complex Ginzburg-Landau equation
• Generalize projective Riccati equation method
• Quadratic–cubic law
• Nonlinear waves
• Anti-cubic law
• Generalized anti-cubic law