Resonant solitons, breather waves, lump waves, and interaction solutions for a (3 + 1)-dimensional pKP-BKP equation

This paper presents a comprehensive investigation of an integrable (3+1)-dimensional pKP-BKP equation, a novel model that synthesizes the potential Kadomtsev-Petviashvili (pKP) and B-type Kadomtsev-Petviashvili (BKP) equations. The equation is highly applicable for modeling nonlinear wave phenomena, including oceanic surface waves and atmospheric disturbances, as it effectively captures the intricate interplay between dispersion and nonlinearity in multi-dimensional wave propagation. Using Hirota’s bilinear method, we first derive the three-soliton solution and analyze its nonlinear superposition mechanism and propagation dynamics, thereby identifying distinct interaction patterns. By strategically annihilating specific dispersion coefficients in the phase shifts, we construct resonant Y -type and X -type solitons. Through a systematic application of the long-wave limit method, we derive lump waves and characterize their dynamics, which are visualized using three-dimensional plots, time-evolving density maps, and trajectory projections. Breather wave solutions are systematically derived by introducing complex conjugate parameters, which reveals explicit amplitude-phase modulation relationships. Furthermore, we analyze the dynamics of localized interaction solutions among these waves, illustrated through dynamical evolution diagrams. This study enhances the understanding of complex nonlinear wave phenomena described by the pKP-BKP equation.