Exact Solutions For Some Nonlinear Evolution Equation

Based on the soliton theory and modern computer technique, this papermainly study some nonlinear evolution equations with physical background byusing the F-expansion method ,homogeneous balance method, and the tanhmethod. With the modern computer technique, we will find their new solitonsolutions and other exact solutions.First of all, we using the F-expansion method , exact solutions of theKlein-Gordon-Zakharov equation in three space dimensions are constructed:The Jacobi ellipse fuction solutions of the equation are obtained.And then, we using a new class of Riccati equation to the same equation, alot of new solutions are obtained.Next,we using the extended tanh-fuction method on a KDV equation,exact solutions of the are obtained.In the following section, we using the recently proposed F-expansionmethod, exact solutions of the Zakharov equation:in three space dimensions are derived.The solutions include sech-solition solutions,tanh-soliton solu-tions,triangle function periodic solutions,rational solutions, and Jacobiellipse fuction solutions, eleven solutions are about five di?erent type of function.Finally, by using the the homogeneous balance method and the F-expansionmethod, we study the {1+1}-dimensional KDV Equations with VariableCoe?cients:the Jacobi ellipse fuction solutions and other type solutions are obtained.