摘要
本文证明,Caudrey-Dodd-Gibbon-Sawada-Kotera方程和Ziber-Shabat-Mikhailov方程的无穷Lie-Bācklund对称序列之列之间存在着一个简单的联系.这一联系是由这样的观察事实所提供的:Ziber-Shabat-Mikhailov 方程和被积修正Caudery-Dodd-Gibbon-Sawada-Kotera 方程的无穷Lie-Bācklund 对称序列是全同的.此外,我们还证明,这一联系是与如下的事实相关的:所有这些方程(包括Cau-drey-Dodd-Gibbon-Sawada-Kotera(cDGSK)方程,修正Caudrey-Dodd-Gibbon-Sawada-Kotera(MCDGSK)方程,被积修正Caudrey-Dodd-Gibbon-Sawada-Kotera(IMCDGSK)方程和Ziber-Shabat-Mikhailov(ZSM)方程)的无穷多守恒律可以变换成同一组具有零Poisson 括号的Virasoro 生成元的多项式函数的无穷集.
It is shown that there exists a simple connection between the infinite sequence of Lie-Bācklund symmetries(written in the form of evolution equations)of the Caudrey-Dood-Gibbon-Sawada-Kotera and the Ziber-Sha-bat-Mikhailov equations.This connection is provided by tbe observation that the infinite sequence of Lie-Back-lund symmetries of the Ziber-Shabat-Mikhailov and the integrated modified Caudrey-Dodd-Gibbon-Sawaba-Kotera equations are identical.Furher,this connection is shown to be related with the fact that infinite conser-vation laws in all these equations are transformed into the same infinite sequence of polynomial functions ofthe Virasoro generators with vanishing poisson brackets;among these are the Caudrey-Dodd-Gibbon-Sawada-Kotera(CDGSK)equation,the modified Caudrey-Dodd-Gibbon-Sawada-Kotera(MCDGSK),the integratedmodified Caudrey-Dodd-Gibbon-Sawada-Kotera and the Ziber-Shabat-Mikhailov(ZSM)equation.
出处
《四川师范大学学报（自然科学版）》
CAS
CSCD
1992年第3期62-73,共12页
Journal of Sichuan Normal University（Natural Science）
