Optical soliton solutions of M-fractional modified complex Ginzburg-Landau equation using unified method: A comparative study

Abstract

The current research investigates the M-fractional modified complex Ginzburg-Landau equation, a crucial nonlinear model for characterizing the behavior and evolution of optical solitary waves in dynamic fiber optics. Examining wave propagation in nonlinear dispersive media is essential since it promotes progress in data transmission for communication systems and allows for generating ultrafast optical pulses. the M-fractional derivative for the MCGL model is applied for the first time, which is more meaningful. The equation is converted into an ordinary differential equation via wave transformation, enabling the use of a unified technique to get many soliton solutions. By applying the unified method, we obtain more solutions than other methods, such as the function transformation technique.²³ The solutions are expressed as tanh,  sec,  tan,  sech functions and their combinations. For the special values of free parameters, we have periodic waves, kinky-periodic waves, periodic lump waves, periodic waves with lump waves, interactions of anti-kink and periodic waves, double periodic waves, and multi-kink waves. This work's innovative component is applying this approach to derive various soliton structures, analyzed using 2D, 3D, and contour representations. Additionally, the influence of fractional parameter presents with 3D plots for γ = 0.1, 0.4, 0.8. we also compare the fractional effect with the classical form in 2D plots. The results highlight the efficacy of this approach in examining soliton solutions in diverse nonlinear models, hence enhancing the comprehension of wave dynamics in mediums with differing stability.