扩展的辅助函数法求一类非线性分数阶偏微分方程的精确解  

Extended Auxiliary Function Method for Exact Solutions of a Class of Nonlinear Fractional Partial Differential Equations

作　　者：张静 ZHANG Jing(School of Applied Mathematics,Nanjing University of Finance and Economics,210023,Nanjing,Jiangsu,China)

机构地区：[1]南京财经大学应用数学学院,江苏南京210023

出　　处：《淮北师范大学学报（自然科学版）》2021年第4期12-17,共6页Journal of Huaibei Normal University：Natural Sciences

基　　金：江苏省自然科学基金:青年基金项目(BK20171040)。

摘　　要：为进一步扩大解的范围,丰富解的结构.文章在前人运用的辅助函数法的基础上做推广,将辅助函数满足的方程扩展到满足一般的Riccati方程上,并借助分数阶复变换和整合的分数阶导数的性质,将该方法运用到求解时间分数阶modified Benjamin-Bona-Mahony(简称mBBM)方程以及(3+1)维非线性分数阶Jimbo-Miwa方程,获得这2个方程的许多新精确行波解.In order to further expand the scope of the solution and enrich the structure of the solution.the article is generalized on the basis of the auxiliary function method used by Yang Jian and Lai Xiaoxia,and the equation satisfied by the auxiliary function is extended to satisfy the general Riccati equation,and with the help of the fractional complex transformation,the method is applied to solve the time fractional modified Benjamin-Bona-Mahony(mBBM)equation and the(3+1)dimensional nonlinear fractional Jimbo-Miwa equation,and many new exact traveling wave solutions are obtained.

关 键 词：分数阶复变换 扩展的辅助函数法 时间分数阶mBBM方程 (3+1)维非线性分数阶Jimbo-Miwa方程 精确行波解 

分 类 号：O175.29[理学—数学]