Solitary-wave solutions of the Klein-Gordon equation with quintic nonlinearity

In this paper, the (G′/G)-expansion method is used to obtain exact solitary-wave and periodic-wave solutions for nonlinear evolution equations arising in mathematical physics with the aid of symbolic computations, namely, the Klein-Gordon equation with quintic nonlinearity. Our work is motivated by the fact that the (G′/G)-expansion method provides not only more general forms of solutions, but also periodic and solitary waves. As a result, hyperbolic function solutions and trigonometric function solutions with parameters are obtained. The method is straightforward and concise, and its application is promising for other nonlinear evolution equations in mathematical physics.