Kaup-Kupershmidt 方程和 Ziber-Shabat-Mikhailov 方程的无穷多守恒律之间的联系(英文)

SIMPLE CONNECTION BETWEEN INFINITE CONSERVATION LAWS IN THE KAUP-KUPERSHMIDT AND THE ZIBER-SHABAT-MIKHAILOV EQUATIONS

本文给出了 Ziber-Shabat-Mikhoilov 方程和 Kaup-Kupershmidt 方程的无穷多守恒量之间的一个简单的关系.我们发现,这个结果是与这样一个事实相关的:与这二个方程相应的二组守恒量可以改写成具有零 Poisson 括号的 Virasoro 生成元的多项式函数的同一组无穷集.

A simple connection is presented between an infinite set of conserved quantities in both the Ziber-Shabat- Mikhailov and the Kaup-Kupershmidt equations.This resuit is found to be related with the fact that both sets in the Ziber-Shabat-Mikhailov and the Kaup-Kupershmidt equations may be reexpressed in terms of the same infinite set of polynomial functions of the Virasoro generators with vanishing Poisson brackets.