New exact solutions of some non-linear evolution equations via functional variable method

Abstract

In recently, many successfull methods have been developed to attain analytical solutions of partial differential equations. In this study, we attained some new exact solutions of the non-linear coupled Klein-Gordon system and non-linear modified Benjamin-Bona-Mahony equation which seems in the various engineering and scientific fields such as plasma physics ,biophysics, and fluid dynamics, by using functional variable method (FVM). Also by using the Mathematica program, we have drawn three dimensional graphics of the obtained solution functions for examined the physical behaviors. The advantage of this method is generate more solutions than other analytical methods. This shows that functional variable method is effective and can be used to solve the equations of evolution in engineering and mathematical physics.