首次积分法求时空-分数阶MkdV-ZK方程新的精确解  

New Exact Solutions of the Space-Time-Fractional mKdV-ZK Equation by First Integral Method

作　　者：张燕 陈兆蕙 ZHANG Yan;CHEN Zhao-hui(Department of Accounting,Guangzhou College of Technology and Business,Guangzhou 510850,China;School of Computer Engineering,Guangzhou College of South China University of Technology,Guangzhou 510800,China)

机构地区：[1]广州工商学院会计系,广东广州510850 [2]华南理工大学广州学院计算机工程学院,广东广州510800

出　　处：《数学的实践与认识》2020年第13期243-250,共8页Mathematics in Practice and Theory

基　　金：广东省普通高校特色创新类项目(2018KTSCX269);广州工商学院2018年科研课题(KA201835);2019年广州工商学院质量工程高等教育教学改革项目(ZL20191120)。

摘　　要：为了给物理学中的动力学行为研究提供依据,更好解释一些物理现象.首先使用分数阶复变换将时空-分数阶MKdV-ZK方程转换为非线性常微分方程组,其次使用除法定理寻求常微分方程组的首次积分,最后使用首次积分求解出原方程的许多精确解,得到了时空-分数阶MKdV-ZK方程的新精确解.数值结果表明首次积分法是有效的,该方法具有简单便捷等优点.To provide evidence for dynamic behavior research in physics and better explain some physical phenomena,firstly,space-time and fractional mKdV-ZK equation can be converted into the non-fractional ordinary differential equations by fractional complex transformation;Secondly,the first integral of ordinary differential equations is sought by using the division theorem.Finally,many exact solutions of the original equation are solved by using the first integral.Many exact solutions of the space-time fractional mKdV-ZK equation are obtained.The results show that the first integral method has great effect on solving the space-time fractional mKdV-ZK equation,and it has the advantages of simplicity and convenience.

关 键 词：时空-分数阶MKdV-ZK方程 除法定理 首次积分法 精确解 

分 类 号：O175.29[理学—数学]