AKNS-KN孤子方程族的可积耦合与Hamilton结构  

Integrable Couplings and Hamiltonian Structure of the AKNS-KN Soliton-Equation Hierarchy

作　　者：张玉峰[1] 郭福奎[2] 

机构地区：[1]辽宁师范大学数学学院,大连116029 [2]山东科技大学信息学院,青岛266510

出　　处：《数学学报（中文版）》2008年第5期889-900,共12页Acta Mathematica Sinica：Chinese Series

基　　金：国家自然科学基金资助项目(10471139)

摘　　要：首先通过引入高维圈代数,在零曲率方程框架下得到了AKNS-KN孤子族(记为AKNS-KN-SH)的一个新的可积耦合系统;再由二次型恒等式得到了该系统的双-Hamilton结构形式.最后引进了一个新的Lie代数A_4,可通过建立其不同的圈代数与等价的列向量Lie代数,研究AKNS-KN-SH的多分量可积耦合系统及其Hamilton结构.By introducing a higher-dimensional loop algebra, a new integrable coupling of the AKNS-KN soliton hierarchy （called AKNS-KN-SH, for short） is obtained under the framework of zero curvature equations, whose Hamiltonian structure is worked out by using the quadratic-form identity. Finally we give a new Lie algebra A4 so that its various loop algebras and its equivalent colummn-vector Lie algebra are introduced respectively for which multi-component integrable couplings and their Hamiltonian structure of the the AKNS-KN-SH could be generated.

关 键 词：HAMILTON结构 圈代数 可积耦合 

分 类 号：O175.29[理学—数学]