Bounded Exact Solutions for Klein-Gordon Equations with Five Orders Nonlinear Terms

Using undetermined coefficient method we obtain bounded exact periodic wave solutions in fractional form of Jacobi elliptic function for Klein-Gordon equations which has nonlinear terms of five orders. Bell-shaped solitary wave solutions and exact periodic wave solutions in cosine function fractional form are also presented, point out that three couples of periodic wave solutions may change into two bell-shaped solitary wave solutions, and four solutions may change into four periodic wave solutions in cosine function form, and some other solutions change into some constants. Further, the dynamical behaviors of these solutions are discussed and it is shown relationship of these exact wave solutions corresponding to planar systems and evolvement relations between periodic wave solutions and solitary wave solutions.