Decomposition Method for Kdv Boussinesq and Coupled Kdv Boussinesq Equations

Abstract

This paper obtains the solitary wave solutions of two different forms of Boussinesq equations that model the study of shallow water waves in lakes and ocean beaches. The decomposition method using He’s polynomials is applied to solve the governing equations. The travelling wave hypothesis is also utilized to solve the generalized case of coupled Boussinesq equations, and, thus, an exact soliton solution is obtained. The results are also supported by numerical simulations.

Keywords: Decomposition Method, He’s polynomials, cubic Boussinesq equation, Coupled Boussinesq equations