利用分数阶(G′G)展式法构造分数阶KdV-Burger方程方程的精确行波解

Construction of Exact Traveling Solutions of Fractional KdV-Burger Equation Using the Fractional(G′ G) Method

(G′G)展式法是一种行之有效的求解分数阶偏微分方程的方法.利用行波变化与齐次平衡技巧可以对该方法进行拓展,拓展后的方法能够处理更一般的分数阶偏微分方程.最后将拓展后的方法应用到基于黎曼-刘维尔积分意义下的时间空间分数阶KdV-Burger方程中,通过符号计算可以得到方程的精确行波解。与其他方法相比,拓展的(G′G)展式法不需要进行变换和数值逼近,计算更加的简洁。

（G′ G） expansionmethod is an effective method for solving fractional partial differentialequations.The method can be extended by using the traveling wave variation andthe homogeneous balance technique,and the extended method can be used to dealwith the more general fractional partial differential equations.Finally,theextended method is applied to the time space fractional KdV-Burger equationbased on the Liu Weier Riemann integral, and the exact traveling wave solutionsof the equations can be obtained by the symbolic computation. Compared withother methods,（G′ G） expansionmethod don＇t need to doing transform and numerical approximation,so thecalculation is more simple.