求解具有任意高次非线性项的Gardner方程和BBM方程的辅助方程法(英文)  

Auxiliary Equation Method for Generalized Gardner Equation and BBM Equation with Nonlinear Terms of Any Order

作　　者：杨丽英[1] 

机构地区：[1]内蒙古农业大学理学院,内蒙古呼和浩特010018

出　　处：《内蒙古师范大学学报（自然科学汉文版）》2012年第5期456-461,共6页Journal of Inner Mongolia Normal University(Natural Science Edition)

基　　金：Project Supported by the National Natural Science Foundation of China(11262017)

摘　　要：通过假设一类辅助椭圆方程解的形式,利用计算机符号计算软件MATHEMATIC,求得该辅助椭圆方程的若干有理函数解和准有理函数解,即由三角函数、双曲函数、椭圆函数和指数函数等与有理函数构成的复合函数形式的解,对应于非线性方程的孤立波解、周期波解和双周期波解.利用该辅助椭圆研究了具有任意高次非线性项的广义Gardner方程和广义Benjamin-Bona-Mahony(BBM)方程,给出一些新的组合形式的解.Through proposing type of solutions of an auxiliary elliptic equation,and using the symbolic computation program such as Mathematic,some new quasi-rational function solutions of the elliptic equation are obtained.These solutions possess the forms of composite functions of rational functions and trigonometric functions,hyperbolic functions,power functions,elliptic functions and so on,which correspond to solitary wave solutions,periodic solutions and bi-periodic solutions.Using this auxiliary elliptic equation,the generalized Gardner equation and Benjamin-Bona-Mahony（BBM） equation with nonlinear terms of any order are investigated,some new solutions of them are obtained.

关 键 词：辅助方程法 广义Gardner方程 广义BBM方程 准有理函数解 

分 类 号：O175.14[理学—数学]