Abstract
The higher order of nonlinear partial differential equations in mathematical physics is studied. We used the analytical mathematical methods of the nonlinear (3+1)-dimensional extended Zakharov-Kuznetsov dynamical, modified KdV-Zakharov-Kuznetsov and generalized shallow water wave equations to demonstrate the efficiency and validity of the proposed powerful technique. The shallow water wave models have been applied in tidal waves and weather simulation. Exact wave solutions of these models in various forms such as Kink and anti-Kink solitons, bright-dark soliton, solitary wave and periodic solutions are constructed that have plenty of applications in diverse areas of physics. Graphically, we presented the movement of some obtained solitary wave solutions that aids in understanding the physical phenomena of these models.