Exact solutions of Boussinesq equations using differential transform method combined with Adomian polynomials

Abstract

The problem addressed in this paper is to obtain new exact solitary solutions for the Boussinesq-like B(m,n) equations with fully nonlinear dispersion. The exact solitary wave solutions can be used to specify initial data for the incident waves in the Boussinesq numerical model and for the verification of the associated computed solution. We use differential transform method. The nonlinear terms can be handled by the use of Adomian polynomials. The proposed technique is general and can be easily modified to solve a wide range of Boussinesq-like equations in coastal engineering.