Complex dynamics, sensitivity analysis and soliton solutions in the (2+1)-dimensional nonlinear Zoomeron model

Abstract

This paper delves deeply into the investigation of the (2+1)-dimensional nonlinear Zoomeron model. The primary focus of the study revolves around comprehending the dynamic behaviors inherent to this model. This is achieved through a thorough exploration of bifurcations occurring at equilibrium points. The paper also effectively demonstrates the model’s propensity for chaotic behavior by employing principles rooted in chaos theory. Furthermore, the paper conducts a meticulous sensitivity analysis of the dynamical system. This analysis utilizes the RK4 method to establish that even minor deviations in initial conditions exert minimal influence on the overall stability of the solution. Additionally, the study employs the comprehensive discrimination system of the polynomial method. This is done systematically to construct individual traveling wave solutions for the governing model. The culmination of these findings contributes to the establishment of a robust and dynamic mathematical framework. This framework can be effectively employed to address a wide spectrum of nonlinear wave phenomena.