Abstract
This manuscript is a captivating exploration of the (3+1)-D nonlinear extended Quantum Zakharov–Kuznetsov (NLEQZK) equation, revealing its complex dynamics and solitary wave solutions. We unveil the general method behind this equation and transform it into an ordinary differential equation (ODE), then venture further by using the Galilean transformation to create a system of ODEs. Further, we journey through bifurcations, chaos, and other fascinating dynamical properties, culminating in the visualization and analysis of solitary wave solutions. From the elegant W-shaped solitons to singular solitons with unconventional characteristics and hybrid singular and periodic solitons, each is discussed in vivid detail. This work presents a significant advancement in understanding the unpredictable and intricate behavior of the model, inviting readers to explore the captivating world of non-linear waves and dynamical systems.
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