系数依赖于时间的KdV-MKdV-Burgers方程的Painlevé性质

THE PAINLEV(?) PROPERTY OF THE TIME-DEPENDENT COEFFICIENT KdV-MKdV-BURGERS EQUATION

近几年来,人们发现非线性偏微分方程的完全可积性和解在奇异流形处的性质密切相关.一个常微分方程解的可移奇点如果都是极点则称为具有Painleve性质.19世纪Painleve曾系统研究了二阶常微分方程的有关性质,而Kowalevskaya揭示了可积性和Painleve性质的联系.Ablowitz、Ramani和Segur猜测如果一个偏微分方程的所有相似约化得到的常微分方程都具有Painleve性质,则是完全可积方程.1983年Weiss、

The conditions that the time-dependent coefficient KdV-MKdV-Burgers equation couldhave Painleve property are discussed. It is proved that this equation can be transformed towell-known solvable equations if it has Painleve property.