Bifurcation, Chaos, Multistability, Sensitivity, and Dynamic Properties to the Third Fractional WBBM Equation

ABSTRACT The third fractional 3D Wazwaz–Benjamin–Bona–Mahony (WBBM) equation is examined in this paper, along with new waveforms and various analyses. This is important for understanding how waves move in plasma physics, shallow water, and nonlinear optics. We use a Galilean transformation to obtain the research output of this model. The planner dynamic system of the equation is also constructed, and all possible phase portrait analyses are described, including bifurcation and chaos. We observed chaotic, periodic, and quasi‐periodic behaviors by introducing a perturbed term for various parameter values. This study talks about multistability analysis, sensitivity analysis, and exact traveling wave solutions of the governing model. Fractal dimension, strange attractor, recurrence plot, power spectrum, return map, and Lyapunov exponent (LE) are some of the graphs that show how the model works. Additionally, this research work employs the unified solver technique to yield diverse solitary‐wave outcomes. We visually display the derived outcomes in 2D and 3D plots. We can conclude that these findings provide a solid foundation for further investigation and are valuable, useful, and reliable for dealing with future complex nonlinear problems. The approach employed in this work demonstrates a high level of reliability, robustness, and efficiency, making it suitable for addressing a vast area of nonlinear partial differential equations (NLPDEs) that have not been studied in any other research.