  In this paper, we consider a kind of shallow water wave model called the
Kadomtsev-Petviashvili-Benjamin-Bona-Mahony (KP-BBM) equation. We firstly
consider the unperturbed KP-BBM equation. Then by using the geometric singular
perturbation (GSP) theory, especially the invariant manifold theory, method of
dynamical system and Melnikov function, the existence of solitary wave
solutions of perturbed KP-BBM equation is proved. In other words, we dissuss
the equation under different nonlinear terms. Finally, we validate our results
with numerical simulations.
