Stability analysis of forced nonlinear wave systems in optical and fluid media.

This study aims to examine the nonlinear features of electromagnetic pulses that propagate obliquely to an external magnetic field within the nonlinear Zakharov Kuznetsov modified equal-width equation. This research will contribute to understanding the complicated dynamical nature of the presented model that implies different areas of research. Our objective is to show the traveling wave solution and stability analysis of the dynamic system. A modified Sardar sub equation technique is applied to find the traveling wave solution of the underlying problem. The traveling wave solution is obtained in a broad variety including solitons, kinks, periodic solutions, rational solutions, and many others. The dynamical analysis starts with phase portraits which provides information to the qualitative dynamics of the system and its stability features. The sensitivity analysis will examine the influence of parameters on the model to provide insights that demonstrate the effectiveness of the model and to examine the behavior of the dynamical system under different initial conditions. We also investigate the chaotic dynamics to identify the stability and categorize periodic, quasi-periodic, and chaotic dynamics of the perturbed dynamical system. These analyses demonstrate the potential application and enhance the underlying mechanics in the field of optical and nonlinear physics. This dynamical analysis improves understanding of nonlinear models and develops efficient mechanisms to manage the complex nonlinear model. Furthermore, Poincare map and Lyapunov exponent are used to find qualitative behavior and visualize the phase space to illustrate the various dynamical regimes. These contributions enhance the improvement in the field of optical soliton and help to analyze the complex dynamical system in the field of engineering and mathematical physics.