与含有三个位势矩阵谱问题相联系的非线性发展方程族及其Hamilton结构

从含有三个位势的4×4矩阵谱问题出发,导出两类非线性发展方程.然后利用迹公式,给出了这两类方程的广义Hamilton结构.     

色散长波方程簇的Hamilton结构

本文导出了色散长波方程簇,并利用屠规彰迹恒等式方法,讨论它们的Hamil-ton结构。     

可积的与Hamilton形式的NLS-MKdV方程族

本文基于ｌｏｏｐ代数Ａ２的一个特殊子代数，设计了一个等谱问题，应用屠规彰格式计算出一族具有Ｈａｍｉｌｔｏｎ结构的可积系．此族含有非线性Ｓｃｈｒｄｉｎｇｅｒ方程与修正的ＫｄＶ方程，称之为ＮＬＳ ＭＫｄＶ方程族     

新的Liouville完全可积的广义Burgers方程族及其Hamilton结构

基于屠格式,从一个新的等谱问题,本文获得了一族广义Ｂｕｒｇｅｒｓ 方程及其Ｈａｍ ｉｌｔｏｎ 结构．最后证明了该族方程是Ｌｉｏｕｖｉｌｌｅ 完全可积的,并且有无穷多个彼此对合的公共守恒密度     

广义KN方程族及其Hamilton结构

构造了一个带有任意光滑函数的等谱问题,利用屠规彰格式得到广义KN 方程族及其Hamilton结构,并且当f=0时,变为著名的KN谱,当f=-12qr时,变为Qiao谱.     

一个新的离散的演化方程族及其Hamilton结构

A new discrete isospectral problem is introduced, from which a hierarchy of Laxintegrable lattice equation is deduced. By using the trace identity, the correspondingHamiltonian structure is given and its Liouville integrability is proved.     

Lax表示的变形与Hamilton方程族的Lax表示

本文首先给出了构造演化方程族的Ｌａｘ表示的马文秀方法的一种变形，后对这一方法作了改进，使之适用于Ｈａｍｉｌｔｏｎ形式的方程族．作为应用，得到了具有非等谱Ｌａｘ表示的杨方程族．     

一个新的Lie代数和它的应用

通过构造一个新的Lie代数,利用它相应的Loop代数设计等谱Lax对,根据其相容性条件,得到了一族Lax可积方程族,其一种约化形式为著名的AKNS族．根据迹恒等式得到该方程族的Hamilton结构．利用该可积方程族可以进一步研究它的达布变换、对称、代数几何解等相关性质．     

带附加项KdV方程族的双Hamilton结构(英文)

通过将ｔ看作空间变量，将ｘ作为发展参数，本文给出了带附加项的ＫｄＶ和ＭＫｄＶ方程族的ｔ型Ｈａｍｉｌｔｏｎ结构。再利用ｔ型Ｍｉｕｒａ变换，得到了带附加项ＫｄＶ方程族的第二个Ｈａｍｉｌｔｏｎ结构，进而构造出遗传算子及一族新的无穷维可积Ｈａｍｉｌｔｏｎ系统，并给出了带附加项的孤立子方程及孤立子方程的约束系统间Ｈａｍｉｌｔｏｎ结构的约化关系．     

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．     

Integrable couplings of fractional L‐hierarchy and its Hamiltonian structures

Based on a general isospectral problem of fractional order, a fractional bilinear form variational identity, the new integrable coupling of fractional L‐hierarchy and the Hamiltonian structures of the integrable coupling of fractional L‐hierarchy are obtained. Copyright © 2016 John Wiley & Sons, Ltd.     

Comparison criteria of positive solutions for a neutral difference equation with positive and negative coefficients

1.IntroductionInthispaper,weareconcernedwithaclassofneutraltypeflorenceequationswithpositiveandnegativecoefficielltsoftheformwhere',TandaarepositiveintegerssuchthatT2a){r'}:,isarealsequence3{p'}:,and{qn}Zoarenonnegativesequences.Similarequationshaver...     

Integrable coupling hierarchy and Hamiltonian structure for a matrix spectral problem with arbitrary-order

We presented an integrable coupling hierarchy of a matrix spectral problem with arbitrary order zero matrix r by using semi-direct sums of matrix Lie algebra. The Hamiltonian structure of the resulting integrable couplings hierarchy is established by means of the component trace identities. As an example, when r is 2 × 2 zero matrix specially, the integrable coupling hierarchy and its Hamiltonian structure of the matrix spectral problem are computed.     

具有正负系数的中立型微分方程的振动性

研究具有正负系数的中立型微分方程（x(t)-Cx(t-r)‘ px(t-τ)-qx(t-σ)=0,在允许C q(τ-σ)≤1不成立的条件下,建立了方程（*）的振动性准则。     

A generalized super AKNS hierarchy associated with orthosymplectic Lie superalgebra OSP(2,2) and its super bi-Hamiltonian structures

For the orthosymplectic Lie superalgebra $\text{◂⋅▸}OSP(2,2)$, we choose a set of basis matrices. A linear combination of those basis matrices presents a spatial spectral matrix. The compatible condition of the spatial part and the corresponding temporal parts of the spectral problem leads to a generalized super AKNS (GSAKNS) hierarchy. By making use of the supertrace identity, the obtained GSAKNS hierarchy can be written as the super bi-Hamiltonian structures.     

Generalized Fractional Trace Variational Identity and A New Fractional Integrable Couplings of Soliton Hierarchy

Based on fractional isospectral problems and general bilinear forms, the generalized fractional trace identity is presented. Then, a new explicit Lie algebra is introduced for which the new fractional integrable couplings of a fractional soliton hierarchy are derived from a fractional zero-curvature equation. Finally, we obtain the fractional Hamiltonian structures of the fractional integrable couplings of the soliton hierarchy.     

An integrable coupling hierarchy of the Mkdv_integrable systems, its Hamiltonian structure and corresponding nonisospectral integrable hierarchy

A four-by-four matrix spectral problem is introduced, locality of solution of the related stationary zero curvature equation is proved. An integrable coupling hierarchy of the Mkdv_integrable systems is presented. The Hamiltonian structure of the resulting integrable coupling hierarchy is established by means of the variational identity. It is shown that the resulting integrable couplings are all Liouville integrable Hamiltonian systems. Ultimately, through the nonisospectral zero curvature representation, a nonisospectral integrable hierarchy associated with the resulting integrable couplings is constructed.