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 nonzero free parameters. These parameters provide broad flexibility 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 fluid mechanics, plasma physics, and nonlinear optics.