NEW EXACT SOLUTIONS FOR THE KLEIN-GORDON EQUATION

Abstract

In this paper, we applied the improved Bernoulli sub-equation function method for the Klein-Gordon equation. Firstly, we reduced the equation to a nonlinear ordinary differential equation by the aid of wave transform. Then we have been obtained various new exact solutions via the method. For some solutions, we drew two and three-dimensional graphics to understand physical behaviors. Nonlinear evolution equations (NLEEs) are widely used because it finds application in many nonlinear disciplines such as plasma physics, optical fibers, fluid mechanics, fluid dynamics and so on. One of the best known of these equations is Klein-Gordon equation(KGE).