Equal-Time and Equal-Space Poisson Brackets of the N-Component Coupled NLS Equation  

作　　者：周汝光 李佩瑶 高媛 

机构地区：[1]School of Mathematics and Statistics,Jiangsu Normal University,Xuzhou 221116,China

出　　处：《Communications in Theoretical Physics》2017年第4期347-349,共3页理论物理通讯（英文版）

基　　金：Supported by National Natural Science Foundation of China under Grant Nos.11271168 and 11671177;by the Priority Academic Program Development of Jiangsu Higher Education Institutions;by Innovation Project of the Graduate Students in Jiangsu Normal University

摘　　要：Two Poisson brackets for the N-component coupled nonlinear Schrdinger(NLS) equation are derived by using the variantional principle. The first one is called the equal-time Poisson bracket which does not depend on time but only on the space variable. Actually it is just the usual one describing the time evolution of system in the traditional theory of integrable Hamiltonian systems. The second one is equal-space and new. It is shown that the spatial part of Lax pair with respect to the equal-time Poisson bracket and temporal part of Lax pair with respect to the equal-space Poisson bracket share the same r-matrix formulation. These properties are similar to that of the NLS equation.

关 键 词：integrable system the N-component coupled nonlinear Schrdinger equation equal-time Poisson bracket equal-space Poisson bracket r-matrix 

分 类 号：O175[理学—数学]