Exact Solutions Of Nonlinear Mathematical Physics Equations F Expansion Method

The nonlinear mathematical physics equations have an important value of theoretic and practice in modern scientific research, and to obtain their exact solutions has been one of the most interests of mathematicians and physicists. During the past four decades or so, the scientists have created various ingenious methods to construct exact solutions, especially soliton solutions of nonlinear mathematical physics equations, among others such as the famous inverse scattering method and Backlund transformations which are remarkable and distinguished successes in the research field of nonlinear mathematical physics. F-expansion method proposed more recently by professor Wang Mingliang is also a very useful method which can be used to solve many types of nonlinear mathematical physics equation, from nonlinear evolution equations with constant coefficients to ones with variable coefficients, from a single nonlinear equation to a system of nonlinear equations, from (1+1)-dimensional equations to (n+1) (n>1) dimensional ones. In this work, numbers of nonlinear mathematical physics equations proposed in modern science and technology, such as KdV equation, nonlinear Schrodinger equation, variant Boussinesq equations, KdV equation with variable coefficients, undamped single pendulum equation of motion, Ginzburg-Landau equation, n-dimensional Klein-Gorden equation, Liouville equation, Sinh-Gordon equation, compound KdV-Burgers equation, have been solved, and abundant periodic wave solutions have been obtained. By using the F-expansion method, without calculating Jacobi elliptic functions, we obtain simultaneously many periodic wave solutions expressed by various Jacobi elliptic functions for the considered equation(s). When the modulus m approaches to 1 or 0, then the hyperbolic function solutions (including the solitary wave solutions) and trigonometrical function solutions are also given.