Soliton solutions with bifurcation, sensitivity, chaotic and stability analysis of the (2+1)-dimensional Zoomeron equation using generalized Riccati equation mapping method

The paper provides a dynamical study of the (2+1)-dimensional Zoomeron equation using the generalized Riccati equation mapping method. By applying an appropriate traveling wave transformation, the equation is reduced to an ordinary differential equation, enabling the construction of various solutions. There are several types of soliton solutions exhibited by the analysis including kink, anti-kink, bell structure or bright solitons, periodic soliton, anti-bell shape or dark soliton and W-shape soliton, singular periodic shape, singular bell shape and V-pattern solutions in terms of hyperbolic and trigonometric functions. The solutions prove rich in understanding the nonlinear wave phenomena of the Zoomeron model. Nonlinear dynamics are investigated using bifurcation, chaotic, sensitivity and stability analysis that uncover complex solution behaviors and stability regimes. This work first and exclusively presents new V-pattern and W-shaped soliton solutions of the (2+1)-dimensional Zoomeron equation by using considered method and offers the first systematic study of their transition from periodic to chaotic behavior. Modulation instability analysis verifies the stability of soliton structures against perturbations. To demonstrate the features and evolution of the solutions, detailed graphical representations are presented, such as 3D surface plots, 2D profiles and contour plots. These visualizations demonstrate the dynamic behaviors and structural properties of the resultant soliton solutions, exemplifying the efficiency of the generalized Riccati equation mapping method for studying intricate nonlinear systems.