Dynamical analysis and exact solutions of a coupled Maccari system: Dynamical insights into chaos, multistability, and nonlinear wave evolution

Abstract

The nonlinear complex coupled Maccari system (CCMS) is a significant model in optics, quantum mechanics, plasma physics, hydrodynamics and some other fields. This paper focuses the analytical and dynamical properties of a nonlinear CCMS. For analytical insight, check the nonlinear behavior and closed-form solutions are obtained using the modified Khater method. These solutions applied in the explanation of the stationary and propagating wave motions. The deeper dynamical analysis is performed with the time-series trajectories, Poincar & eacute; sections, bifurcation diagrams, and Lyapunov exponents to classify the dynamic complex states of the system. The system exhibits transitions from periodic to quasi-periodic and chaotic responses with parameter variation, along with multistability and coexisting attractors due to softening and hardening nonlinearities. In addition, advanced diagnostic tools such as power spectrum analysis, fractal dimension, return maps, and recurrence plots are employed to rigorously characterize the system behavior. These techniques confirm the emergence of chaos and provide deeper insight into the geometric and spectral properties of the underlying attractors. The graphical representations clearly illustrate the transitions between regular and chaotic dynamics, as well as regions of multistability. Overall, this work establishes a unified analytical-computational framework for the investigation of higher-dimensional nonlinear evolution equations. The findings offer significant theoretical contributions and hold potential applications in fluid dynamics, nonlinear optics, and plasma physics.