An efficient computational technique for class of generalized Boussinesq shallow-water wave equations

Abstract

In this study, a modification of the homotopy perturbation method called the homotopy perturbation transform method (shortly, HPTM) is applied to the generalized Boussinesq and generalized perturbed Boussinesq equations. These equations depict the propagation of long waves in shallow water under gravity, one-dimensional nonlinear lattices, and nonlinear strings. They are also significantly important in coastal and ocean engineering. The numerical simulations have been implemented to verify that the proposed scheme is very reliable and accurate. Significant results and their graphical depictions revealed that HPTM is more appropriate for nonlinear problems, and it is immensely active for nonlinear models of classical and fractional order type. The obtained results illuminate that the proposed method is simple to implement and very effective to analyze the complex models arising in science, technology, and engineering.