This research investigates the application of the Riccati-Bernoulli (R-B) sub-ODE technique to analyze the (3+1)-dimensional Boiti-Leon-Manna-Pempinelli (BLMP)  and the three-dimensional Potential Yu-Toda-Sasa-Fukuyama (3D-PYTSF) equations. By integrating traveling wave transformations with the R-B framework, both equations are systematically reduced to algebraic systems. Various soliton solutions, including kink-type, singular, and periodic solutions, are derived. To visualize the physical significance of these solutions, 3D plots, density graphs, and contour diagrams are generated based on appropriate parameter selections. The R-B sub-ODE method proves to be an effective yet straightforward technique for addressing nonlinear partial differential equations (NLPDEs).