Optical soliton solutions for time-fractional Ginzburg–Landau equation by a modified sub-equation method

Abstract

In the present work, we employed a novel modification of the Sardar sub-equation approach, leading to the successful derivation of several exact solutions for the time-fractional Ginzburg–Landau equation with Kerr law nonlinearity. These solutions encompass a range of categories, including singular, wave, bright, mixed dark–bright, and bell-shaped optical solutions. We demonstrate the dynamic behavior and physical significance of these optical solutions of the proposed model via several graphical simulations, including contour plots, three-dimensional (3D) graphs, and two-dimensional (2D) plots. Furthermore, we investigate the magnitude of the time-fractional Ginzburg–Landau equation by analyzing the influence of the conformable fractional order derivative and the impact of the time parameter on the newly constructed optical solutions. The proposed technique is a generalized form that incorporates various methods, including the improved Sardar sub-equation method, the modified Kudryashov method, the tanh-function extension method, and others. To the best of our knowledge, these solutions are novel and have not been reported in the literature. Moreover, the present method is efficient and robust for analyzing applied differential equations in plasma physics and nonlinear optics.