This study investigates the generalized ( \(3+1\) )-dimensional P-type equation governing plasma wave evolution and instabilities. Various localized wave structures, including N-soliton solutions, resonant solitons, breathers, lump waves, and hybrid waves, are derived and analyzed. Using Hirota’s bilinear method, the bilinear form is obtained, allowing the identification of N-soliton solutions and the exploration of soliton interactions, particularly soliton collisions. Resonant localized waves, such as soliton molecules, are studied through velocity resonance mechanisms, revealing interesting bound-state behaviors. The N-soliton solutions are transformed into breathers of varying orders via the parameter complexification method. Lump waves of different orders are derived by limiting the N-soliton solutions. Hybrid waves are constructed by combining localized wave solutions from partial degeneration of N-soliton solutions. Dynamic behaviors of these waves are analyzed through 3D visualizations, uncovering novel structures and properties. This work provides new insights into the model, with implications for fields like fluid mechanics, optical fibers, ocean dynamics, and applied physics.
