Exact Solutions For Some Nonlinear Evolution Equation

In this paper, we mainly use the soliton theory and method such as ho-mogeneous balance method, the extended tanh method , Jacobi elliptic functionmethod and F-expansion method, Modified F-expansion method, to study somenonlinear evolution equations with physical background. Based on previous studywork, we obtain their new soliton solutions and new exact solutions.At first, we study the coupled nonlinear Klein-Gordon equation as follows byusing modified Jacobi elliptic function methodφtt ?φ+ m1φ= (a11|φ|2 + a12|ψ|2)φ,ψtt ?ψ+ m2ψ= (a21|φ|2 + a22|ψ|2)ψ,and we construct a series of new periodic solutions. In the limit cases, these solu-tions degenerate to solitary solutions. And we also construct abundant exact solu-tions of the equation as mentioned above by using modified F-expansion method.Next, by using F-expansion method, we study two kinds of coupled equa-tions with important physical background, and construct their new exact solu-tions . These equations are as follows1, (1+1)-dimension coupled Klein-Gordon-Zakharov(K-G-Z) equation...