This study investigates the temporal evolution of obliquely propagating resonant optical solitons in a (3 + 1)-dimensional framework governed by the resonant nonlinear Schrödinger equation with Kerr-law nonlinearities. Two analytical methods, the \(\:\left(\frac{F}{\mu\:F+G}\right)-\) expansion method and the sine-Gordon expansion method, are employed to explore and extract the soliton solutions of the equation under study. The obtained soliton solutions are analysed through two- and three-dimensional graphs, providing vivid insights into their localized and stable structures, as well as interactions and propagation dynamics that are otherwise difficult to discern analytically. A diverse range of wave profiles is observed, including singular solitons, bright and dark-bright solitons, multi-soliton structures, and periodic waves, highlighting the rich dynamical behaviour of the system. Bifurcation behaviour associated with the existence of traveling waves is also examined by reformulating the considered equations into a planar dynamical system. Chaotic behaviour analysis and sensitivity analysis of the resulting dynamical system are also presented.
