Lump collision dynamics in the generalized (3 + 1)-dimensional variable coefficient B-type Kadomtsev-Petviashvili equation

Abstract This paper investigates the physical characteristics of different types of traveling wave solutions to the generalized (3 + 1)-dimensional variable coefficient B–type Kadomtsev-Petviashvili (KP) equation. This equation plays a significant role in modeling nonlinear phenomena in fluid dynamics, mathematical physics, and engineering sciences. Using the Hirota bilinear method, we reveal distinctive solutions, including lump-periodic, two-wave, breathing wave, and rogue wave solutions. These wave phenomena are significant for understanding complex systems and hold practical significance in fields such as oceanography and nonlinear optics, where rogue waves make challenges due to their abrupt and daring nature. Through broad 3D and contour plots, we effectively illustrate the intricate physical properties of these solutions, underscoring their relevance in the study and prediction of nonlinear behaviors across various scientific domains. The results presented provide valuable paths for further research into the dynamic processes governing natural and engineered systems.