Lie symmetries and dynamics of invariant solutions to (3 + 1)-dimensional KP-BBM equation

This article aims to analyze Lie symmetries and provide analytical solutions to the generalised form of the (3 + 1)-dimensional Kadomtsev–Petviashvili Benjamin–Bona–Mahony equation. The test equation can be employed in energy harvesting systems, transportation, the oil and gas industry, and maritime engineering. The similarity transformations method via Lie group theory is utilized to derive infinitesimal generators, and hence similarity form is obtained, which turns the test equation into an equivalent ordinary differential equation. Under appropriate parametric constraints, the ordinary differential equation provides a variety of exact solutions. We trace the profiles of the solutions to emphasize their physical significance, demonstrating their dark lump, doubly soliton, stationary, bright soliton, and line multisoliton natures. Moreover, we determine the novelty and generality of the derived solutions by comparing them to the previous outcomes. The results of this study could be useful in different fields, such as ionic-acoustic solitons, coastal engineering for modeling and assessing long surface gravity waves, and in the computer simulation of nonlinear systems.