一个新的Liouville可积方程族及其双Hamilton结构

辽宁石油化工大学学报 ›› 2013, Vol. 33 ›› Issue (2): 88-92.

一个新的Liouville可积方程族及其双Hamilton结构

于义

(抚顺师范高等专科学校,辽宁抚顺113001

收稿日期:2012-12-12 出版日期:2013-06-25 发布日期:2017-07-14
作者简介:于义(1962灢),男,辽宁新宾县,副教

A New Liouville Integrable Hierarchy and Its BiHamiltonian Structure

YU Yi

Fushun Teachers College,Fushun Liaoning 113001,China

Received:2012-12-12 Published:2013-06-25 Online:2017-07-14

摘要/Abstract

摘要： 寻找新的可积方程族在孤立子理论中是十分重要的。首先,构造了一个新的方程族,利用高维Lie代
数A2 及其相应的loop代数煋A2,证明了此方程族是Lax可积的。其次,利用迹恒等式构造了Lax可积方程族的双
Hamilton结构。最后,获得了此方程族的无穷多守恒密度,证明了此方程族为Liouville可积的。

关键词: Lie代数 , 可积系统 , Hamilton结构

Abstract: It is important to search for new integrable equations hierarchies in soliton theory. First, a new equations hierarchy was constructed. Taking use of higherdimension Lie algebra A2 and the corresponding loop algebra [AKA~]2, it was proved that the equations hierarchy is Lax integrable. Then, the biHamiltonian structures of the Lax integrable hierarchy were constructed by making use of the trace identity. Finally, the infinitely conserved densities for the equations hierarchy was obtained and it was proved that the Lax equations hierarchy is Liouville integrable.

Key words: Lie algebra , Integrable system , Hamiltonian structure

于义. 一个新的Liouville可积方程族及其双Hamilton结构[J]. 辽宁石油化工大学学报, 2013, 33(2): 88-92.

YU Yi. A New Liouville Integrable Hierarchy and Its BiHamiltonian Structure[J]. Journal of Liaoning Petrochemical University, 2013, 33(2): 88-92.