The Extended Hyperbolic Function Method And Exact Solutions Of Nonlinear Equations

In this paper, hyperbolic tangent function method and its some extensions suchas sine-cosine method, extended tanh method, F-expansion method and Jacobi ellip-tic function method are summarized, the idea and technique of hyperbolic functionmethod are explored. Based on the studies, some important nonlinear mathemat-ical physics equations are studied. Firstly, Sine-Gordon equation,Tzitzeica-Dodd-Bullough equation, Dodd-Bullough-Mikhailov equation , Liouville equation, and ageneralized long-short wave equation are reduced by some transformations. And thenthe exact solutions of these equations with more general form are obtained by usingthe extended hyperbolic function method proposed recently by shang. These solutionsinclude some entirely new solitary wave solutions, singular traveling wave solutions,and periodic traveling wave solutions.