超Kaup-Newell族的非线性可积耦合及其超哈密顿结构

Nonlinear integrable couplings of super Kaup-Newell hierarchy and its super Hamiltonian structures

基于一类新的Lie超代数,介绍了构造超孤子族非线性可积耦合的一般方法.由相应圈超代数上的超迹恒等式,可以得到超孤子族非线性可积偶的超哈密顿结构.作为应用,给出了超Kaup-Newell族的非线性可积耦合及其超哈密顿结构,这种方法还可以推广到其他的超孤子族.

Based on a kind of new Lie superalgebras, we introduce the general method of constructing the nonlinear integrable couplings of super soliton hierarchy. Super trace identity over the corresponding loop superalgebras is used to obtain the super Hamiltonian structures for the resulting nonlinear integrable couplings of the super soliton hierarchy. As an application, we give the nonlinear integrable couplings of super Kaup-Newell hierarchy and its super Hamiltonian structures. This method can be generalized to other super soliton hierarchy.