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To the non-linear Klein-Gordon equations, the undetermined assumption method is used to get the exact periodic wave solution in the form of Jacobi elliptic function fraction and with the asymptotic values non-zero. The condition for their existence and boundness are obtained and the impact of the change of travelling periodic wave velocity is revealed upon the periodic wave solution and the size of the period. Keywords-Nonlinear Klein-Gordon equation, Jacobi elliptic function, Periodic wave solutions

New Exact Periodic Wave Solutions of the Nonlinear Klein-gordon Equation