利用H am ilton对称群的作用不变量,将R4N上具有标准辛结构的双非线性化T oda特征值问题约化为R4N/(R>0)N上L ie-Po iss on结构下的3×3非线性化特征值问题;并进一步讨论了该3×3非线性化特征值问题与R2N上标准辛结构下的2&#...利用H am ilton对称群的作用不变量,将R4N上具有标准辛结构的双非线性化T oda特征值问题约化为R4N/(R>0)N上L ie-Po iss on结构下的3×3非线性化特征值问题;并进一步讨论了该3×3非线性化特征值问题与R2N上标准辛结构下的2×2非线性化特征值问题之间的关系.展开更多
By resorting to the nonlinearization approach, a Neumann constraint associated with a discrete 3 × 3 matrix eigenvalue problem is considered. A new symplectic map of the Neumann type is obtained through nonlinear...By resorting to the nonlinearization approach, a Neumann constraint associated with a discrete 3 × 3 matrix eigenvalue problem is considered. A new symplectic map of the Neumann type is obtained through nonlinearization of the discrete eigenvalue problem and its adjoint one. The generating function of integrals of motion is presented, by which the symplectic reap＇is further proved to be completely integrable in the Liouville sense.展开更多
The method of nonlinearization of spectral problem is developed and applied to the discrete nonlinear Schr6dinger （DNLS） equation which is a reduction of the Ablowitz-Ladik equation with a reality condition. A new i...The method of nonlinearization of spectral problem is developed and applied to the discrete nonlinear Schr6dinger （DNLS） equation which is a reduction of the Ablowitz-Ladik equation with a reality condition. A new integable symplectic map is obtained and its integrable properties such as the Lax representation, r-matrix, and invariants are established.展开更多
By means of the theory of harmonic maps into the unitary group U(N), the authors study harmonic maps into the symplectic group Sp(N). The symplectic uniton and symplectic ex--tended uniton are introduced. The method o...By means of the theory of harmonic maps into the unitary group U(N), the authors study harmonic maps into the symplectic group Sp(N). The symplectic uniton and symplectic ex--tended uniton are introduced. The method of the symplectic Backlund transformation and the Darboux transformation is used to construct new symplectic unitons from a known one.展开更多
A symplectic reduction method for symplectic G-spaces is given in this paper without using the existence of momentum mappings. By a method similar to the above one, the arthors give a symplectic reduction method for t...A symplectic reduction method for symplectic G-spaces is given in this paper without using the existence of momentum mappings. By a method similar to the above one, the arthors give a symplectic reduction method for the Poisson action of Poisson Lie groups on symplectic manifolds, also without using the existence of momentum mappings. The symplectic reduction method for momentum mappings is thus a special case of the above results.展开更多
By choosing a discrete matrix spectral problem, a hierarchy of integrable differential-difference equations is derived from the discrete zero curvature equation, and the Hamiltonian structures are built. Through a hig...By choosing a discrete matrix spectral problem, a hierarchy of integrable differential-difference equations is derived from the discrete zero curvature equation, and the Hamiltonian structures are built. Through a higher-order Bargmann symmetry constraint, the spatial part and the temporal part of the Lax pairs and adjoint Lax pairs, which we obtained are respectively nonlinearized into a new integrable symplectic map and a finite-dimensional integrable Hamiltonian system in Liouville sense.展开更多
基金The project supported by National Natural Science Foundation of China under Grant No. 10471132 and the Special Foundation for the State Key Basic Research Program ＂Nonlinear Science＂
文摘By resorting to the nonlinearization approach, a Neumann constraint associated with a discrete 3 × 3 matrix eigenvalue problem is considered. A new symplectic map of the Neumann type is obtained through nonlinearization of the discrete eigenvalue problem and its adjoint one. The generating function of integrals of motion is presented, by which the symplectic reap＇is further proved to be completely integrable in the Liouville sense.
基金Supported by National Natural Science Foundation of China under Grant No. 10871165
文摘The method of nonlinearization of spectral problem is developed and applied to the discrete nonlinear Schr6dinger （DNLS） equation which is a reduction of the Ablowitz-Ladik equation with a reality condition. A new integable symplectic map is obtained and its integrable properties such as the Lax representation, r-matrix, and invariants are established.
基金Project supported by the National Natural Science Foundation of China (No.19531050)the Scientific Foundation of the Minnstr
文摘By means of the theory of harmonic maps into the unitary group U(N), the authors study harmonic maps into the symplectic group Sp(N). The symplectic uniton and symplectic ex--tended uniton are introduced. The method of the symplectic Backlund transformation and the Darboux transformation is used to construct new symplectic unitons from a known one.
文摘A symplectic reduction method for symplectic G-spaces is given in this paper without using the existence of momentum mappings. By a method similar to the above one, the arthors give a symplectic reduction method for the Poisson action of Poisson Lie groups on symplectic manifolds, also without using the existence of momentum mappings. The symplectic reduction method for momentum mappings is thus a special case of the above results.
基金Supported by the National Basic Research Program of China (973) Funded Project under Grant No. 2011CB201206
文摘By choosing a discrete matrix spectral problem, a hierarchy of integrable differential-difference equations is derived from the discrete zero curvature equation, and the Hamiltonian structures are built. Through a higher-order Bargmann symmetry constraint, the spatial part and the temporal part of the Lax pairs and adjoint Lax pairs, which we obtained are respectively nonlinearized into a new integrable symplectic map and a finite-dimensional integrable Hamiltonian system in Liouville sense.
