Relationship Between the Restricted AKNS Flows and the Restricted KdV Flows  

作　　者：Ruguang ZHOU 

机构地区：[1]School of Mathematical Sciences,Xuzhou Normal University,Xuzhou 221116,Jiangsu,China.

出　　处：《Chinese Annals of Mathematics,Series B》2012年第2期191-206,共16页数学年刊（B辑英文版）

基　　金：Project supported by the National Natural Science Foundation of China (No.10871165)

摘　　要：It is well-known that every member of the KdV hierarchy of equations can be obtained from the AKNS hierarchy of equations by imposing a simple reduction. The author finds that the reduction conditions of the potentials in the spectral problem can be replaced by adding additional eigenfunction equations to the spectral problem, and then shows that the restricted KdV flows, such as the Neumann system, the Gamier system and the generalized multicomponent Henon-Hieles system, are a kind of special reductions of the restricted AKNS flows.

关 键 词：The restricted AKNS flow The restricted KdV flow Nonlinearization ofspectral problem Reduction condition Integrable Hamiltonian system 

分 类 号：O175.9[理学—数学] TK124[理学—基础数学]