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(2+1)维KdV族的可积耦合及其哈密顿结构
引用本文:宋明,徐建建,徐秀丽.(2+1)维KdV族的可积耦合及其哈密顿结构[J].曲阜师范大学学报,2009,35(1):29-32.
作者姓名:宋明  徐建建  徐秀丽
作者单位:宋明,SONG Ming(荣成市第二中学,264309,荣成市);徐建建,XU Jian-jian(山东科技大学信息科学与工程学院,266510,青岛市);徐秀丽,XU Xiu-li(枣庄科技职业学院,277500,山东省滕州市)  
摘    要:首先构造了一个loop代数;根据(2+1)维零曲率方程计算得到(2+1)维KdV族的可积耦合,然后通过二次型恒等式得到它的哈密顿结构.展示的方法新颖简便,可以用于其它许多方程族.

关 键 词:(2+1)维零曲率方程  二次型恒等式  可积耦合  哈密顿结构

Integrable Couplings of the (2+1)-Dimensional KdV Hierarchy and its Hamiltonian Structure
SONG Ming,XU Jian-jian,XU Xiu-li.Integrable Couplings of the (2+1)-Dimensional KdV Hierarchy and its Hamiltonian Structure[J].Journal of Qufu Normal University(Natural Science),2009,35(1):29-32.
Authors:SONG Ming  XU Jian-jian  XU Xiu-li
Institution:SONG Ming, XU Jian-jian, XU Xiu-li (1. Rongcheng No. 2 Middle School,264309, Rongcheng; 2. College of Information Science and Engineering, Shandong University of Science and Technology,266510, Qingdao ; 3. Zaozhuang College of Vocational Technology,277500,Tengzhou, Shandong, PRC )
Abstract:A loop algebra is constructed,whose subalgebra can be used to present a lax pair.Using the(2+1)-dimensional zero curvature equation,integrable coupling of the(2+1)-dimensional hierarchy is generated.Further more,the Hamilton ian structure of its integrable couplings is worked out by using of the quadratic-form identity,which is of Liouville intergrable.The method mentioned can be widely used to other soliton hierarchies.
Keywords:(2 + 1 ) -dimensional zero curvature equation  quadratic-form identity  integrable coupling  Hamil- tonian structure  
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