Abundant closed-form and solitonic wave solutions of the nonlinear Boussinesq equation: Bifurcation, chaotic behavior and sensitivity analysis

Abstract

The modified extended Fan sub-equation methodology is utilized in this research to obtain solitary wave solutions for the Boussinesq equation. This approach describes a slightly nonlinear model with extended amplitude. As a result, by making suitable assumptions for the constants, several solutions are discovered. These comprise the Wpattern, Z-pattern, kink pattern, anti-kink pattern, bell pattern, anti-bell pattern and plane pattern solitary wave solutions. To illustrate the computational analysis of the obtained solutions using the proposed technique, various graphical representations, including 2D, 3D, and contour plots, are presented. In addition, phase portrait analysis is performed, and the system is converted into a planar dynamical system. Furthermore, sensitivity analysis of the dynamical system indicates that small variations in the initial conditions do not significantly affect the stability of the solutions. By introducing a perturbation parameter into the dynamical system, the presence of chaotic dynamics in the model is also investigated.