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

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.