一类NLS-mKdV方程族的扩展可积系统  

A type of expanding integrable system for NLS-mKdV hierarchy

作　　者：张玉峰[1] 闫庆友[2] 

机构地区：[1]山东科技大学信息学院数学研究所 [2]山东财政学院经济统计系,济南250014

出　　处：《物理学报》2003年第9期2109-2113,共5页Acta Physica Sinica

摘　　要：利用代数变换 ,构造了与文献 [5 ]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 ,结合子代数间的直和运算和同构关系 ,得到了NLS_mK dV方程族的一类扩展可积系统 .作为约化情形 ,求得了著名的SchrA subalgerbra (A) over bar (1), which is equivalent to the subalgebra of the loop algebra (A) over tilde (2) in '1997 Acta Math. Sin. 40 801', is constructed by making use of algebraic transformation. Then a high-dimensional loop algebra (G) over tilde is presented in terms of (A) over bar (1). An isospectral problem is established following (G) over tilde by the use of direct sum operators and isomorphic relations among subalgebras. It follows that a type of expanding integrable system for the NLS-mKdV hierarchy of evolution equations is obtained. As in reduction cases, the integrable couplings of the famous Schrodinger equation and mKdV equation are presented.

关 键 词：NLS-mKdV方程族 扩展可积系统 代数变换 LOOP代数 等谱问题 可积耦合系统 孤立子 

分 类 号：O411[理学—理论物理]