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首页> 外文期刊>Applied mathematics and computation >F-expansion method and its application for finding new exact solutions to the sine-Gordon and sinh-Gordon equations
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F-expansion method and its application for finding new exact solutions to the sine-Gordon and sinh-Gordon equations

机译：F展开方法及其在寻找Sine-Gordon和sinh-Gordon方程的新精确解中的应用

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摘要

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.
机译：在本文中，基于F展开法和F展开法的扩展版本，我们分别研究了Sine-Gordon方程和sinh-Gordon方程的精确解。首先，引入了几种特殊的变换将正弦-戈登方程和正弦-戈登方程变为多项式非线性发展方程。然后用F展开法及其扩展形式求解这些多项式非线性发展方程。最后，明确构造了更多新的精确Jacobian椭圆函数解和孤子解。

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