Investigation of optical soliton solutions of (1+1)-dimensional complex Ginzburg-Landau equation having the Kudryashov's law of self-phase modulation

In this paper, we investigate the optical soliton solutions of the (1+1)-dimensional complex Ginzburg–Landau equation incorporating Kudryashov's law of self-phase modulation. By applying a suitable complex wave transformation, the governing equation is reduced to nonlinear ordinary differential equations for the cases n=1 and n=2, and analytical solutions are obtained using the unified Riccati equation expansion method. To our knowledge, this is the first study to address the complex Ginzburg–Landau equation with the Kudryashov's law parameter, highlighting its novelty and relevance. As a result, a variety of soliton types, bright, dark, and kink solitons, are obtained under specific parametric constraints. The physical characteristics of these solutions are illustrated through two-dimensional, three-dimensional, and contour plots, offering clear insight into their behavior. Overall, the findings demonstrate the effectiveness of the proposed method for analyzing evolution equations with complex nonlinearity and provide new perspectives on soliton dynamics in nonlinear optical systems.