Dispersive and propagation of shallow water waves as a higher order nonlinear Boussinesq-like dynamical wave equations

The propagation of small amplitude long capillary gravity waves on the surface of shallow water described by the higher order nonlinear Boussinesq type wave equation. This model is arising in mathematical physics, shallow water waves, fluid dynamics and fluid flow. We applied the modified Jacobi elliptic function expansion method to obtained exact solutions in the type of solitary wave and elliptic functions solutions. These solutions helps the mathematicians and physicians to understand the physical phenomena of this model. This technique can be utilized on other models to launch further exclusively novel solutions for other categories of nonlinear PDEs occurring in mathematical Physics. (C) 2019 Elsevier B.V. All rights reserved.