Qualitative Analysis And Exact Solutions For Nonlinear Klein-Gordon Equation

There are threefold word in this paper. Firstly, we studied the solutions of Klein-Gordon equation forΦ4-Φ3 model with using the qualitative analysis theory and give some corresponding phase portraits of system. Secondly, we construct exact solutions for nonlinear Klein-Gordon equation by using the first integral method. Thirdly, auxiliary differential equation method and improved generalized auxiliary differential equation method are employed to establish exact solutions of nonlinear Klein-Gordon equation forΦ4+Φ3 model and generalized Klein- Gordon equation. Many new solutions which include rational function solutions, trigonometric function solutions, hyperbolic function solutions and periodic solutions are obtained in this work.