中文摘要：

首先研究了基于Kac-Moody代数sl（2,C[λ~（-1）,λ）获得一类新的谱问题.得到的谱问题可以视为AKNS谱问题的一个推广,由此可以引出耦合Burgers方程族.作为该方程族的可积特征得到了多Hamilton结构、无穷多对称和守恒律.耦合Burgers方程具有两个局部的Hamilton算子,基于此,给出3个相容的Hamilton算子并且得到一个耦合Burgers方程的3-Hamilton对偶系统.此外,建立了一个联系所研究的谱问题与AKNS谱问题的规范变换,基于该变换还讨论了Burgers方程族与一个约化的AKNS方程族的关系.

英文摘要：

In this paper, we investigate a kind of spectral problems which are based on the frame of Kac-Moody algebra sl（2, C[λ-1, λ]）. We present a spectral problem which can be viewed as a generalization of the AKNS spectral problem and generate a coupled Burgers hierarchy. We provide integrabilities of the hierarchy, such as multi-Hamiltonian structures and infinitely many symmetries and conservation laws. The coupled Burgers system has two local Hamiltonian operators, based on which we give three compatible Hamiltonian operators. A tri-Hamiltonian dual system of the coupled Burgers equations is presented. Besides, a gauge transformation that connects our spectral problem and the AKNS spectral problem is constructed. The relation between the Burgers hierarchy and a reduced AKNS hierarchy is also discussed.