The Kadomtsev-Petviashvili-Benjamin-Bona-Mahony (KP-BBM) model equations as
a water wave model, are governing equations, for fluid flows, describes
bidirectional propagating water wave surface. The soliton solutions for
(2+1) and (3+1)-Dimensional Kadomtsev-Petviashvili-Benjamin-Bona-Mahony
(KP-BBM) equations have been extracted. The solitary wave ansatz method are
adopted to approximate the solutions. The corresponding integrability
criteria, also known as constraint conditions, naturally emerge from the
analysis of the problem.