一个新的loop代数及相应的一族可积系

A new loop algebra and its corresponding integrable system

构造了一个复数 loop代数 A*1 ,由此设计了一个复的Lax对,根据其相容性得到了一族新的可积系.再利用迹恒等式,求出了该可积系的分解Hamilton结构.作为约化情形,获得了一个类似于AKNS族的可积系统.

A loop algebra _1~* in the complex number form is constructed.On this basis,a complex Lax pair is designed, whose compatibility gives rise to a new hierarchy of evolution equations.By using trace identity, the decomposed Hamiltonian structure of the above hierarchy is worked out.As a reduction case, an integrable system analogous to AKNS hierarchy is obtained.