几个非线性发展方程的精确解  

The Exact Solutions for Some Nonlinear Evolution Equation

作　　者：杨娟[1] 曾春花[1] 冯庆江[1] YANG Juan ZENG Chun-hua 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19期229-236,共8页Mathematics in Practice and Theory

基　　金：国家自然科学基金(11464023);贵州省卓越教师教育培养计划(数学与应用数学)(201525);凯里学院2014年重点学科(数学)(KZD2014004)

摘　　要：应用改进F/G展开法求得(2+1)维BBM方程、(1+1)维Benjiamin Ono方程、广义(2+1)维ZK-MEW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,可得到孤立波解:当对三角函数解中的参数取特殊值时,可得到周期波函数解.实践表明,F/G展开法在非线性发展方程中具有广泛的应用.Using the extended F/G expansion method, exact solution for（2＋1）-dimensional BBM equation,（1＋1）-dimensional Benjiamin Ono equation, generalized（2＋1）-dimensional ZK-MEW equation were constructed. 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 the extended F/G expansion method has a very wide range of application in the study of nonlinear evolution equations.

关 键 词：F/G展开法 (2+1)维BBM方程 (1+1)维Benjiamin Ono方程 广义(2+1)维ZK-MEW方程 精确解 

分 类 号：O175.29[理学—数学]