Abstract
The extended simple equation method is applied to construct solitary wave solutions of (3 + 1)-dimensional Kadomtsev-Petviashvili-Benjamin-Bona-Mahony (KP-BBM), Korteweg-de Vries Benjamin-Bona-Mahony (KdV-BBM), Breaking soliton (BS) and (2 + 1) Maccari system waves system of equations. These models have prevalent usage in modern science. This technique can also be functional to solve different kinds of nonlinear evolution problems in contemporary areas of research. It is an effective and powerful mathematical tool in finding solitary wave solutions of nonlinear evolution equations (NLEEs) in mathematical physics.