一族离散的可积Hamilton方程与可积的辛映射

该文讨论一个新的离散特征值问题，导出了相应的离散的Hamilton系统的保谱族，并且证明了它们是Liouville可积系。通过谱问题的双非线性化，导出一个新的可积的辛映射 。      

Integrable deformations of integrable symplectic maps

A method of generating integrable deformations of integrable symplectic maps is presented. The integrable deformations of the integrable Toda symplectic map, the integrable Volterra symplectic map and the integrable Ablowitz–Ladik symplectic map, as well as their Lax representations are obtained.     

Relationship Between the Restricted AKNS Flows and the Restricted KdV Flows

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 ...     

一个求孤子方程有限带势解的方法

基于Lax对非线性化方法，我们以KdV方程为例给出了一个构造孤子方程的有限带势解的方法．通过Lax对非线性化KdV方程被分解成两个有限维可积系统，进而找到这些有限维可积系统公共的角-作用坐标，最终我们获得了KdV方程的有限带势解．     

Nonlinearization of the Lax pairs for discrete Ablowitz-Ladik hierarchy

The discrete Ablowitz-Ladik hierarchy with four potentials and the Hamiltonian structures are derived. Under a constraint between the potentials and eigenfunctions, the nonlinearization of the Lax pairs associated with the discrete Ablowitz-Ladik hierarchy leads to a new symplectic map and a class of finite-dimensional Hamiltonian systems. The generating function of the integrals of motion is presented, by which the symplectic map and these finite-dimensional Hamiltonian systems are further proved to be completely integrable in the Liouville sense. Each member in the discrete Ablowitz-Ladik hierarchy is decomposed into a Hamiltonian system of ordinary differential equations plus the discrete flow generated by the symplectic map.     

多分量AKNS方程的新可积分解

从一个任意阶矩阵谱问题出发,多分量AKNS方程的新可积分解被导出.通过利用迹恒等式建立了其双哈密顿结构.同时,证明了空间与时间的约束流在刘维尔意义下是两个完全可积的哈密顿系统.