Bifurcation analysis and new waveforms to the first fractional WBBM equation

This research focuses on bifurcation analysis and new waveforms for the first fractional 3D Wazwaz-Benjamin-Bona-Mahony (WBBM) structure, which arises in shallow water waves. The linear stability technique is also employed to assess the stability of the mentioned model. The suggested equation's dynamical system is obtained by applying the Galilean transformation to achieve our goal. Subsequently, bifurcation, chaos, and sensitivity analysis of the mentioned model are conducted by applying the principles of the planar dynamical system. We obtain periodic, quasi-periodic, and chaotic behaviors of the mentioned model. Furthermore, we introduce and delve into diverse solitary wave solutions, encompassing bright soliton, dark soliton, kink wave, periodic waves, and anti-kink waves. These solutions are visually presented through simulations, highlighting their distinct characteristics and…