Solitary wave solutions of the delayed KP-BBM equation

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.