Solution to Nonlinear Wave and Evolution Equations by Direct ALgebraic Method

Abstract

This work presents a dynamic and systematic step-by-step method for constructing solitary
wave solutions for non-dissipative nonlinear evolution and wave equations from the real exponential solutions of the underlying linear equations. The work reviewed the direct algebraic method initially proposed by Hereman et. al. (1985) and employed the methodology in solving Benjamin - Bona - Mahony (RLW) equation and Joseph - Egri (TRLW) equation. By the method which involves using a traveling frame of reference to convert the PDE into an ODE and solving the ODE by algebraic processes; we obtained solutions for the Benjamin - Bona - Mahony and the Joseph - Egri equations. This method was found to be efficient in constructing
a single solitary wave solution for non-dissipative evolution equations. The results obtained in this paper are in agreement with those obtained using other methods.