A Class of Two-Component Adler-Bobenko-Suris Lattice Equations

We study a class of two-component forms of the famous list of the Adler-Bobenko-Suris lattice equations. The obtained two-component lattice equations are still consistent around the cube and they admit solutions with ＇jumping properties＇ between two levels.     

基于约束流的Kaup-Newell方程的Darboux变换的非线性化

本文研究Kaup-Newell方程的Darboux变换的非线性化.基于Kaup-Newell方程的Darboux变换经过非线性化得到的映射是约束Kaup-Newell流的Bcklund变换的假设,本文获得了Darboux矩阵中的位势与特征函数之间的约束,由此实现了Kaup-Newell方程的Darboux变换的非线性化,生成了4个具有相同不变量的可积辛映射.     

A Bcklund Transformation of the Restricted mKdV Flow with a Rosochatius Deformation

A Bcklund transformation of the restricted mKdV flow with a Rosochatius deformation is constructed.Its Lax representation and thus N invariants in involution are presented.Such Bcklund transformation is a Rosochatius deformation of that of the restricted mKdV flow.     

双约束孤立子流的可积形变

提出了基于Lax矩阵的构造双约束孤立子流的可积形变的新方法.作为应用,导出了双约束KdV流和双约束mKdV流的可积形变,并给出了这些形变的Lax表示、r-矩阵和守恒积分.     

双约束孤立子流的可积形变

提出了基于Lax矩阵的构造双约束孤立子流的可积形变的新方法.作为应用,导出了双约束KdV流和双约束mKdV流的可积形变,并给出了这些形变的Lax表示、r-矩阵和守恒积分.     

Neumann型约束Tu流的r矩阵和分离变量

本文发展了适用于Neumann型约束流的r矩阵方法．研究了Neumann型约束Tu流．获得了Neumann型约束Tu流的Lax表示；证明了在Dirac括号下这个Lax算子满足r矩阵关系，从而再次证明了Neumann型约束Tu流是Liouville完全可积的．另外，还利用r矩阵关系，找到了这个Neumann型约束流的一组正则变量，从而把Neumann型约束Tu流线性化．     

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．     

An Integrable Decomposition of the Derivative Nonlinear SchrSdinger Equation

The nonlinearization method of spectral problem is developed and applied to the derivative nonlinear Schr6dinger equation （DNLS）. As a result, an integrable decomposition of the DNLS equation is obtained.     

Integrable Rosochatius Deformations of the Restricted cKdV Flows

Three novel finite-dimensional integrable Hamiltonian systems of Rosochatius type and their Lax representations are presented. We make a deformation for the Lax matrbces of the Neumann type, the Bargmann type and the high-order symmetry type of restricted cKdV flows by adding an additional term and then prove that this kind of deformation does not change the r-matrix relations. Finally the new integrable systems are generated from these deformed Lax matrices.