Burgers-KdV方程的系列解析解  

Series of analytic solutions for Burgers-KdV equation

作　　者：刘韡[1] 郭婧[1] 姜昊天[1] 颜心力[1] 

机构地区：[1]西安建筑科技大学理学院,陕西西安710055

出　　处：《西北大学学报（自然科学版）》2014年第4期521-524,共4页Journal of Northwest University（Natural Science Edition）

基　　金：国家自然科学基金资助项目(51178387)

摘　　要：Burgers方程与KdV方程是流体领域中的两个重要方程,Burgers-KdV方程具有丰富的内涵,是许多领域内研究内在规律的控制方程。首先用行波变换,将Burgers-KdV控制方程化为非线性常微分方程,接着采用辅助方程法、双曲余切函数展开法、双曲正切函数展开法、余切函数展开法、正切函数展开法获得新的3种类型孤波解和两种类型的周期波解。这些方法也可以用于求解其他有类似性态的微分方程。Burgers equation and KdV equation are two important equations in fluid field.Burgers-KdV governing equation had rich connotation and was proposed to study the inherent law in many fields.Burgers-KdV equation is changed into nonlinear ordinary differential equations based on travelling wave transformation.As a result,three new types of solitary wave solutions and two types of periodic wave solutions for Burgers-KdV equation are successfully derived by means of auxiliary equation,hyperbolic cotangent function expansion,hyperbolic tangent function expansion,cotangent function expansion and tangent function expansion solution methods.These methods can be used to solve other similar characteristic differential equations.

关 键 词：辅助方程法 双曲函数展开法 三角函数展开法 行波解 

分 类 号：O340[理学—固体力学]