一类非线性广义Schrdinger方程族的扩展可积系统

A class of expanding integrable system for generalized Schrdinger hierarchy

利用代数变换,构造了与文献〔4〕中的Loop代数A2的子代数等价的Loop代数A1的一个子代数A1。再将A1扩展为一个高维的Loop代数G,利用G设计了一个等谱问题,结合子代数间直和运算和同构关系,得到了广义Schrdinger方程族的一类扩展可积系统。作为约化情形,求得了著名的广义Schrdinger方程的可积耦合系统。

A subalgerbra A 1,which is equivalent to the subalgebra of the Loop algebra A2 in [4], is constructed by making use of algebraic transformation, and then a high - dimensional Loop alegebra G is presented in terms of A1. An isospectral problem is established following G by using direct sum operators and isomorphic relations among subalgebras. It is concluded that a class of expanding integrable system for generalized Schrodinger hierarchy of evolution equations is obtained. As in reduction cases, the integrable coupling of the famous generalized Schroedinger e -quation is presented.