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

作　　者：张旭[1] 于宪伟[1] 齐美美[1] 张继明[1] 

机构地区：[1]渤海大学数理学院,锦州121013

出　　处：《渤海大学学报（自然科学版）》2011年第3期215-219,共5页Journal of Bohai University:Natural Science Edition

基　　金：辽宁省教育厅科学研究基金资助项目(No:2010009)

摘　　要：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.

关 键 词：LOOP代数 可积系统 等谱问题 可积耦合 

分 类 号：O175.29[理学—数学]