Structural analysis of multi-dimensional pulse propagation of the KP–Boussinesq model in optical fibers

This research investigates the nonlinear wave propagation through generalized solitary pulses of the (3+1)-dimensional KP-Boussinesq equation using a recently constructed symbolic bilinear technique (SBT). By employing a Cole–Hopf transformation, the equation transforms into a Hirota-type bilinear form containing arbitrary parameters. The SBT enables the systematic generation of generalized single-, double-, and triple-soliton solutions in closed form. It extends classical Hirota solitons by incorporating non-zero free parameters. These parameters provide broad exibility for exploring nonlinear wave dynamics, including phase shifts, collisions, and structural changes of solitons. Comprehensive two- and three-dimensional analyses reveal rich structural behaviors and validate the obtained solutions against known Hirota results. The technique offers a robust symbolic framework for deriving generalized soliton solutions of higher-dimensional nonlinear evolution equations. This work opens a symbolic pathway for analyzing large-parameter nonlinear wave models in higher dimensions, providing a framework extendable to dozens of nonlinear evolution equations in uid mechanics, plasma physics, and nonlinear optics.