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

Two Poisson brackets for the N-component coupled nonlinear Schrdinger（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...

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Bibliographic Details
Published inCommunications in theoretical physics Vol. 67; no. 4; pp. 347 - 349
Main Author 周汝光 李佩瑶 高媛
Format Journal Article
LanguageEnglish
Published 01.04.2017
Subjects
Lax对
变分原理
哈密顿系统
多元非线性
时间演化
泊松括号
空间变量
耦合NLS方程
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ISSN0253-6102
DOI10.1088/0253-6102/67/4/347

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Summary:Two Poisson brackets for the N-component coupled nonlinear Schrdinger（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.
Bibliography:integrable system the N-component coupled nonlinear Schrdinger equation equal-time Poisson bracket equal-space Poisson bracket r-matrix
11-2592/O3
Two Poisson brackets for the N-component coupled nonlinear Schrdinger（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.
ISSN:0253-6102
DOI:10.1088/0253-6102/67/4/347