Symplectic realizations and action-angle coordinates for the Lie–Poisson system of Dirac hierarchy

作者：

Highlights：

• Three symplectic realizations of the Lie–Poisson structure associated with Lie algebra sl(2) are presented.

• The notion can be used to study the relations among the restricted systems related to the same soliton hierarchy.

• The action-angle coordinates and Jacobi inversion problem for the Lie–Poisson Hamiltonian systems are also studied.

• The restricted Dirac system are used as an illustrative example.

摘要

•Three symplectic realizations of the Lie–Poisson structure associated with Lie algebra sl(2) are presented.•The notion can be used to study the relations among the restricted systems related to the same soliton hierarchy.•The action-angle coordinates and Jacobi inversion problem for the Lie–Poisson Hamiltonian systems are also studied.•The restricted Dirac system are used as an illustrative example.

论文关键词：Poisson structure,Restricted system,Symplectic realization,Action-angle coordinates

论文评审过程：Available online 24 July 2014.

论文官网地址：https://doi.org/10.1016/j.amc.2014.06.103