\(F\)-expansion method and its application for finding new exact solutions to the sine-Gordon and sinh-Gordon equations. (English) Zbl 1288.35154
Summary: 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.
MSC:
| 35C05 | Solutions to PDEs in closed form |
| 35L71 | Second-order semilinear hyperbolic equations |
| 35A25 | Other special methods applied to PDEs |
| 35C08 | Soliton solutions |
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