Jacobi elliptic function solutions of nonlinear wave equations via the new sinh-Gordon equation expansion method
Jacobi elliptic function solutions of nonlinear wave equations via the new sinh-Gordon equation expansion method
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DOI：
10.1088/0305-4470/36/7/311
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发表时间：
2003-02
期刊：
影响因子：
--
通讯作者：
Zhenya Yan
中科院分区：
文献类型：
--
作者：
Zhenya Yan
基于著名的sinh-Gordon方程，提出了一种新的sinh-Gordon方程展开方法。该方法将求解非线性偏微分方程的问题转化为求解相应的代数方程组的问题。借助于符号计算，可在计算机上实现。选取了数学物理中的KdV-mKdV方程、（2+1）维耦合Davey-Stewartson方程、新的可积Davey-Stewartson型方程、修正的Boussinesq方程、（2+1）维mKP方程和（2+1）维广义KdV方程等非线性波动方程来说明该方法。结果，得到了许多新的双周期（雅可比椭圆函数）解。当模m → 1或0时，也可得到相应的孤立波解和单周期解，该方法也可用于求解其它非线性微分方程。
In this paper, based on the well-known sinh-Gordon equation, a new sinh-Gordon equation expansion method is developed. This method transforms the problem of solving nonlinear partial differential equations into the problem of solving the corresponding systems of algebraic equations. With the aid of symbolic computation, the procedure can be carried out by computer. Many nonlinear wave equations in mathematical physics are chosen to illustrate the method such as the KdV-mKdV equation, (2+1)-dimensional coupled Davey–Stewartson equation, the new integrable Davey–Stewartson-type equation, the modified Boussinesq equation, (2+1)-dimensional mKP equation and (2+1)-dimensional generalized KdV equation. As a consequence, many new doubly-periodic (Jacobian elliptic function) solutions are obtained. When the modulus m → 1 or 0, the corresponding solitary wave solutions and singly-periodic solutions are also found. This approach can also be applied to solve other nonlinear differential equations.