Abstract
In this paper, based on the F-expansion method and the extended version of F-expansion method we investigate the exact solutions of the sine–Gordon equation and sinh-Gordon equation, respectively. Firstly, several special transformations are introduced to change the sine–Gordon and sinh-Gordon equations into polynomial nonlinear evolution equations. Then these polynomial nonlinear evolution equations are solved by the F-expansion method and its extended version. Finally, more new exact Jacobian elliptic function solutions and soliton solutions are constructed explicitly.
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