一类偏微分方程(组)非古典对称存在性的判定方法  

A DECISION METHOD FOR THE EXISTENCE OF NONCLASSICAL SYMMETRY OF PARTIAL DIFFERENTIAL EQUATIONS

作　　者：朝鲁[1] 银山[2] 

机构地区：[1]上海海事大学文理学院,上海201306 [2]内蒙古工业大学理学院,呼和浩特010051

出　　处：《系统科学与数学》2012年第8期976-985,共10页Journal of Systems Science and Mathematical Sciences

基　　金：国家自然科学基金(11071159,61072147);上海海事大学校基金资助项目(20110008)

摘　　要：基于微分特征集理论和算法,提出在一定条件下判定偏微分方程(组)非古典对称存在性的机械化方法.该方法对Clarkson P A提出的关于偏微分方程(组)的非古典对称的公开问题给出了部分回答,为完全解决该问题提供了一个思路.通过若干个发展方程的非古典对称的确定说明了该方法的有效性.Based on the differential characteristic set theory and algorithm, a mechanical method is proposed to determine the existence of nonclassical symmetry of partial differential equations. By using the method, we get the partial answer for an open problem proposed by Clarkson P A on nonclassical symmetry of partial differential equations and a potential way to completely solve the problem. To illustrate the effectiveness of our method, the nonclassical symmetries of several evolution equations are determined by using the proposed method.

关 键 词：偏微分方程(组) 非古典对称 微分特征列集 判定 机械化算法 

分 类 号：O175.2[理学—数学]