一类方程簇的Painlevé分析  

Painlevé analysis of a kind of equation hierarchy

作　　者：杨志林[1] 

机构地区：[1]合肥工业大学理学院,安徽合肥230009

出　　处：《合肥工业大学学报（自然科学版）》2003年第5期1083-1086,共4页Journal of Hefei University of Technology：Natural Science

摘　　要：对于与二阶多项式等谱问题相联系的方程簇的Painlevé分析,文章利用Weiss、Tabor及Carnevale(简称WTC)等人的方法对方程簇进行Painlevé分析。对m=2、n≥2时的方程簇进行Painlevé分析,给出了递推关系式,从中可得它的所有分支和共振点,给出了可积方程具有Painlevé性质的一个例证。The Painlevé analysis of partial differential equations is made with the methods developed by Weiss,Tabor and Carnevale(WTC) so as to provide a unified approach to the integrable equation hierarchy. As m=2,n≥2,the Painlevé analysis of the equation hierarchy is carried out, and the resonances for all solution branches are obtained. An example of the integrable equation with Painlevé property is given.

关 键 词：PAINLEVE分析 二阶多项式 等谱问题 偏微分方程 分支 共振点 BACKLUND变换 

分 类 号：O175.2[理学—数学]