A Family of Integrable Rational Semi-Discrete Systems and Its Reduction

Within framework of zero curvature representation theory, a family of integrable rational semi-discrete systems is derived from a matrix spectral problem. The Hamiltonian forms of obtained semi-discrete systems are constructed by means of the discrete trace identity. The Liouville integrability for the obtained family is demonstrated. In the end, a reduced family of obtained semi-discrete systems and its Hamiltonian form are worked out.     

A hierarchy of lattice soliton equations and its Darboux transformation

A new discrete spectral problem is introduced and the corresponding hierarchy of the lattice soliton equations are derived by means of the trace identity. We find a new Darboux transformation of the lattice soliton equation, through which the explicit solutions are shown.     

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 。      

关于一个可积的广义Hamilton方程族

本文利用ｒ－矩阵生成了一个广义的Ｈａｍｉｌｔｏｎ方程族，并证明了它是广义可积的，然后讨论了它和（４）中Ｌｉｏｖｖｉｌｌｅ可积的新的广义Ｈａｍｉｌｔｏｎ方程族之间的关系。     

一个新的无限维Liouville可积系及其变换

本文讨论了一个新的等谱特征问题，按屠规彰格式导出了相应的Ｌａｘ可积的非线性发展方程族。证明了它是Ｌｉｏｕｖｉｌｌｅ可积系，并且讨论了谱参数改变符号时相应的可积系的变化情况。     

An extended functional transformation method and its application in some evolution equations

In this paper, an extended functional transformation is given to solve some nonlinear evolution equations. This function, in fact,is a solution of the famous KdV equation, so this transformation gives a transformation between KdV equation and other soliton equations. Then many new exact solutions can be given by virtue of the solutions of KdV equation.     

耦合的AKNS-Kaup-Newell孤子方程族的一类可积扩展模型

基于Lie圈代数?1的子代数建立了一个等谱问题，导出了耦合的AKNS- Kaup- Newell孤子方程族。另外，利用扩展相应Lie代数于?2的方法，建立了该方程族的可积扩展模型，即可积耦合。     

一列Liouville可积的有限维Hamilton系统族

本文直接递归地生成了一列Liouville可积的有限维Hamilton系统族，给出了其一串对合的公共运动积分和一组对合的生成元．     

一族新的Lax可积系及其Liouville可积性

该文讨论了一个新的等谱特征值问题．按屠规彰格式导出了相应的Lax可积的非线性发展方程族，利用迹恒等式给出了它的Hamilton结构并且证明它是Liouville可积的．     

一族新的可积系及其双约束流的Hamilton正则表示

基于一个新的等谱问题，按屠格式导出了一族新的可积系，具有双Hamilton结构，通过建立双对称约束，得到了该方程族的两组约束流，并将其化为正则的Hamilton系统。