一类时空分数阶爆破孤立子方程组的新解法  

A New Method of the Time-Space Fractional Breaking Soliton Equations

作　　者：陈兆蕙 唐跃龙 Chen Zhaohui;TangYueong(School of Computer Engineering,Guangzhou City Institute of Technology,Guangzhou 510800,China;College of Science,Hunan University of Science and Engineering,Yongzhou 425000,Hunan,China)

机构地区：[1]广州城市理工学院计算机工程学院,广州510800 [2]湖南科技学院理学院,湖南永州425000

出　　处：《科技通报》2024年第8期13-21,共9页Bulletin of Science and Technology

基　　金：湖南省自然科学基金项目(2020JJ4323);广州城市理工学院校级科研项目(56-K0223006、56-K0223016)。

摘　　要：为得到一类时空分数阶爆破孤立子方程组的新精确解,本文采用了一种新的解法——拓展的(G'/G)-展开方法。首先通过行波变换,将原分数阶偏微分方程组转化为整数阶非线性常微分方程组,其次结合齐次平衡原理,增加负幂次项,将含有相同次数的幂结合,并令同次幂系数为零,再运用数学软件MATLAB求解相应的系数方程组,得出该方程新的含有参数形式的精确解。结果表明:拓展的(G'/G)-展开方法能丰富这类分数阶偏微分方程的精确解。In order to seek new exact solutions of a class of space-time fractional breaking soliton equations,a new method—the extended(G'/G)-expansion method,is proposed in this paper.First,the original fractional partial differential equations are transformed into integer nonlinear differential equation by traveling wave transformation.Secondly,the theory of homogeneous principle is combined with the addition of negative power terms,and make the same power coefficient to zero,and then use the mathematical software MATLAB to solve the corresponding coefficient equations,new exact solutions of the equations with parameter form are obtained.The results show that the extended(G'/G)-expansion method can enrich the exact solutions of this kind of fractional partial differential equation.

关 键 词：时空分数阶爆破孤立子方程组 拓展的(G'/G)-展开方法 MATLAB软件 新精确解 

分 类 号：O175.29[理学—数学]