The (3+1)-dimensional Kadomtsev-Petviashvili-Boussinesq equation describes the dynamics of water waves, leading to the formation of nonlinear wave structures on controllable backgrounds. It is important to understand these structures for predicting energy localization, wave stability, and severe wave anomalies. In this manuscript, a new (3+1)-dimensional Kadomtsev–Petviashvili–Boussinesq equation with constant coefficients is presented offering a more comprehensive framework for nonlinear waves in water. Using the Hirota bilinear method, explicit N-soliton solutions are derived. These solutions are converted into Y-type resonant soliton solutions, parallel solitons, and breather solutions by imposing distinct resonance conditions. The long-wave limit method is further employed to construct first-, second-, and third-order lump waves, which are rationally localized. Further, several hybrid solutions involving solitons, lumps, and breathers are discussed and their interaction dynamics are studied, providing insight into the various nonlinear phenomena of the equation. These newly explored features may play an essential role in wave theory. This analysis explores the relationships between solution types and their stability under various conditions, suggesting that future research could reveal new phenomena related to nonlinear wave equations.
Ahmed et al. (Fri,) studied this question.