Bifurcation, chaos analysis and soliton solutions to the generalized Zakharov–Kuznetsov–Benjamin–Bona–Mahony equation

This paper explores exact traveling wave solutions of the (2+1)-dimensional generalized Zakharov–Kuznetsov–Benjamin–Bona–Mahony equation, which is significant in fluid dynamics and ocean engineering. This equation models long waves with small yet finite amplitudes in magnetized plasma. By applying a wave transformation, the governing equation is reduced to a nonlinear ordinary differential equation using two established techniques: the unified method and the modified Sardar sub-equation method, incorporating the conformable fractional derivative. Various soliton solutions, including anti-kink, periodic, dark, bright, combo, and singular solitary waves, are derived in rational, hyperbolic, trigonometric, and exponential forms. The study further analyzes the impact of fractional derivatives by varying their parameters. A comprehensive examination of bifurcation, chaos, and stability is performed, with phase portraits highlighting dynamic shifts at critical points. The introduction of an external periodic force induces chaotic behavior, providing deeper insights into wave dynamics. Additionally, 2D and 3D visualizations illustrate the temporal evolution of solutions. All results are validated through MATHEMATICA and MATLAB simulations, ensuring accuracy and applicability to broader nonlinear models in mathematical physics.