Exact chirped solutions, stability analysis and chaotic behaviours of the perturbed nonlinear Schrödinger equation with anti-cubic nonlinearity and spatio-temporal dispersion

Abstract The nonlinear Schrödinger equation (NLSE) has extensive applications in optical fiber communications. In nonlinear fibers, the study of chirped solitons is crucial for achieving long-distance high-speed optical communications. This paper investigates the perturbed NLSE with anti-cubic nonlinearity and spatio-temporal dispersion (STD), which can more accurately describe the effect of particle distance decay. First, I analyzed the qualitative characteristics of soliton solutions using dynamic system theory. Using the complete discrimination system for polynomial proposed by Liu, I obtained various new types of chirped soliton, including rational solutions, elliptic function solutions, singular solutions and so on. Then, I perform numerical simulations of special chirped solitons under given parameters to demonstrate their physical properties. Furthermore, I analyzed the energy of the soliton solution and established its stability conditions. Finally, I studied the chaotic behavior of the equation and found that different perturbation functions lead to significantly different chaotic characteristics, providing corresponding Lyapunov exponents and phase diagrams. These findings contribute to the practical applications of complex nonlinear systems and the development of optical fiber communications.