Chaotic dynamics and diverse chirped solutions in the quadratic-cubic perturbed complex Ginzburg-Landau equation

This paper examines the quadratic-cubic perturbed complex Ginzburg-Landau equation, focusing on its chaotic dynamics under external perturbation terms and the derivation of exact chirped solutions. By utilizing a complex envelope traveling wave transformation, we establish the corresponding dynamic system and analyze its chaotic behaviors. Furthermore, we apply the trial equation method to obtain a comprehensive set of exact chirped solutions, including solitary wave solutions, Jacobi elliptic function double periodic solutions, rational solutions, and singular periodic solutions. Notably, the method allows us to determine the form of solutions based on the physical parameters. These results can be used to fully describe the structure of chirped solutions. Finally, we present graphical representations of these diverse solutions and their chirps, clearly demonstrating the rich dynamical behaviors of the system and how they evolve under different parameter values, consistent with analytical constraints identified. Importantly, the chirped solutions we obtain have direct implications for practical photonic applications such as optical pulse compression, dispersion management in fiber optics, and signal processing in ultrafast laser systems. Moreover, the analysis of chaotic dynamics and the derivation of analytical solutions contribute to addressing key challenges in nonlinear optical systems, including the control of instabilities and the design of robust pulse propagation models. These findings provide both theoretical insights and practical tools for advancing photonic technologies governed by nonlinear wave equations.