用标准和扩展的Tanh函数法求解修正Jaulent-Miodek方程组

Solving Modified Jaulent-Miodek Equations by Tanh Method and Extended Tanh Method

为寻求修正Jaulent-Miodek方程组精确解的合适方法,采用Tanh函数法和扩展Tanh函数法进行求解。研究表明,在对方程组作行波变换的基础上,Tanh函数法假设方程组具有双曲正切函数形式的解,将非线性方程组的求解问题转化为非线性代数方程组的求解;扩展Tanh函数法因在拟设解时增加了负次幂项多项式,从而获得了与Tanh函数法不同形式的精确解;相比于其他方法,标准和扩展的Tanh函数法为直接的代数方法,可简洁、快速地求出精确解。

In order to find a fit method to obtain the exact solutions of the modified Jaulent-Miodek equations,the Tanh function method and the extended Tanh function method are used.The results show that,on the basis of traveling wave transformation of the equations,Tanh function method assumes that the equations have solutions in the form of hyperbolic tangent function,and transforms the solutions of the nonlinear equations into the solutions of the nonlinear algebraic equations,and the extended Tanh function method obtains a different form of exact solution because the negative power polynomial is added in the proposed solution.Compared with others,these two are more direct algebraic methods able to obtain the exact solution in a concise and quick manner.