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

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.