广义的tanh-coth方法在求解一类分数阶非线性偏微分方程中的应用研究  

Application of Generalized Tanh-Coth Method in Solving a Class of Fractional Nonlinear Partial Differential Equations

作　　者：郝孟涵 庞晶[1] HAO Meng-han;PANG Jing(College of Sciences,Inner Mongolia University of Technology,Hohhot 010051,China)

机构地区：[1]内蒙古工业大学理学院

出　　处：《内蒙古工业大学学报（自然科学版）》2019年第3期161-169,共9页Journal of Inner Mongolia University of Technology：Natural Science Edition

基　　金：国家自然科学基金项目(10561151)

摘　　要：本文主要是利用广义的tanh-coth方法去求解分数阶非线性偏微分方程的精确解.因为时间分数阶耦合Drinfel’d-Sokolov-Wilson(DSW)方程精确解的求解方法相对较少,所以以该方程为例,对广义的tanh-coth方法进行研究.该方法通过复变换将分数阶非线性偏微分方程转换成常微分方程,从而得到多组易于计算得到、无需线性化、无小扰动的收敛级数形式的解析解.In this paper,the generalized tanh-coth method is used to obtain the exact solutions of fractional nonlinear partial differential equations.There are relatively few methods for solving the exact solution of the time fractional coupled Drinfel'd-Sokolov-Wilson(DSW)equation,so the generalized tanh-coth method is introduced and studied by taking DSW equation as an example.In this method,the fractional nonlinear partial differential equation is transformed into ordinary differential equation by complex transformation,and the analytical solutions in the form of convergent series,which is easy to calculate and does not need to be linearized and without small disturbances,are obtained.

关 键 词：分数阶耦合Drinfel’d-Sokolov-Wilson(DSW)方程 广义的tanh-coth方法 分数阶导数定义 

分 类 号：O175.2[理学—数学]