标度变换与变系数非线性发展方程的精确解  

Scaling Transformations and Exact Solutions for Several Nonlinear Evolution Equations with Variable Coefficients

作　　者：斯仁道尔吉[1] 

机构地区：[1]内蒙古师范大学数学科学学院,呼和浩特010022

出　　处：《内蒙古大学学报（自然科学版）》2014年第6期569-573,共5页Journal of Inner Mongolia University：Natural Science Edition

基　　金：国家自然科学基金资助项目(10461006;11261037);内蒙古师范大学"十百千"人才培养工程项目(RCPY-2-2012-K-033)

摘　　要：将Cariello和Tabor提出的求解不可积非线性发展方程精确解的方法推广到变系数方程的情形,并通过求解奇异流形函数的约束方程组和由标度变换引出的相似约化方程给出了变系数Burgers方程,变系数KdV-Burgers方程,变系数Newell-Whitehead方程的精确解.The method to solve non-integrable nonlinear evolution equations given by Cariello and Tabor is generalized to the case of variable coefficient equations. The exact solutions for the variable coefficient Burgers equation, KdV-Burgers equation and Newell-Whitehead equation are presented through solving the restricted equations of singular manifold functions and the similarity reduction equations induced from the scaling transformation.

关 键 词：PAINLEVÉ分析 变系数非线性方程 标度变换 

分 类 号：O175.29[理学—数学]