Exact Solutions Of Five Nonlinear Evolution Equations

Constructing the exact solutions of the nonlinear evolution equations isthe important hot spot topic. At present, a lot of methods are proposed to look for theexact solutions of the nonlinear evolution equations. But, there is no an unified wayfor solving nonlinear evolution equations by now. In this paper three effectivemethods are used to obtain the exact solutions of five evolution equations.In the chapter2, the first integral method can be applied to the nonlinearLandau-Ginzburg-Higgs eqution. By means of this method, some exact solutions thenonlinear evolution equation are obtained. In the chapter3and4, the modified simpleequation (MSE) method is implemented to find the exact solutions for the nonlinear(3+1) kadomtsev-petviashvili equation and Vakhnenko-Parkes equation. Theefficiency of this method for constructing these exact solutions has been demonstrated.In the chapter5and6, the simplest equation method has been used for finding theexact solutions of three nonlinear evolution equations, namely the Cahn-Allenequation and (3+1) Zakharov-Kuznetsov equation.