应用改进的简单方程法求非线性数学物理方程的精确解  

Exact Solutions for the Nonlinear Mathematical Physics Equations by Using Modified Simple Equation Method

作　　者：杨娟[1] 黄朝军[1] 冯庆江[1] YANG Juan HUANG Chao-jun FENG Qing-jiang(School of Mathematics Sciences, Kaili University, Kaili 556000, Chin)

机构地区：[1]凯里学院数学科学学院,贵州凯里556000

出　　处：《数学的实践与认识》2017年第10期222-226,共5页Mathematics in Practice and Theory

基　　金：凯里学院2014年重点学科(数学)(项目编号:KZD2014004);凯里学院2014年校级课题项目(Z1424)

摘　　要：应用改进的简单方程法求得Cahn-Allen方程和Jimbo-Miwa方程的精确解,这些解包括双曲函数解、三角函数解.当对双曲函数解中的参数取特殊值时,可以得到了孤立波解.当对三角函数解中的参数取特殊值时,可以得到对应的周期波函数解.实践证明,简单方程法对于研究非线性数学物理方程具有非常广泛的应用意义.Exact solution for the Cahn-Allen equation and Jimbo-Miwa equation is obtained by using the improved simple equation method. These solutions include hyperbolic function solutions, trigonometric function solutions. When the arbitrary parameters in hyperbolic function solutions are taken as some special values, the solitary wave solutions can be obtained.When the arbitrary parameters in trigonometric function solutions are taken as some special values, the trigonometric function solutions can be expressed as periodic wave solutions. Experience has proved that Simple equation method has a very wide range of application in the study of nonlinear mathematical physics equations.

关 键 词：简单方程法 Cahn-Allen方程 JIMBO-MIWA方程 精确解 

分 类 号：O175[理学—数学]