与二阶多项式等谱问题相联系方程的Painlevé分析  

Painlevé analysis of the equation related to the polynomial isospectrum problem

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2期272-276,共5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)等人的方法对方程进行Painlevé分析。当m=2、n=1时,详细给出了方程组的Painlevé分析,阐明了该方程组具有Painlevé性质,并对此Laurent级数截尾展开得到约化的Burgers方程的Ba··cklund变换,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=1, a detailed study of the equations is made, and it is shown that the equations possess the Painlevé property. Furthermore, by the truncated Laurent expansion, the Ba··cklund transformation for the Burgers equations is found. An example of integrable differential equations with Painlevé property is given.

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

分 类 号：O175.29[理学—数学]