BKP方程族的Pfaffian解

本文从约化的角度考虑BKP方程族的Pfaffian形式的解.证明了通过施加适当的微分约束,KP方程族的格拉姆行列式的解很自然的约化为BKP方程族的解.     

BKP方程族的Pfaffian解

本文从约化的角度考虑BKP方程族的Pfaffian形式的解.证明了通过施加适当的微分约束,KP方程族的格拉姆行列式的解很自然的约化为BKP方程族的解.     

孤子族的生成及换位表示的一般结构

本文通过对谱问题ψｘ＝Ｕ（ｕ，λ）ψ的直接研究，利用谱梯度提供一条获得孤子方程族的途径，进一步，我们给出了孤子方程换位表示的一般结构，同时我们还将看到同一个谱问题可产生两族不同的孤子发展方程。     

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．     

方程族的Painlevé相容组的求解公式

利用求解Painlevé相容组,本文得到了求解KdV方程族,Kuperschmidt方程族和CDG方程族的Painlevé相容组的递推公式同时,提供了利用Painlevé相容组寻求孤立子方程族的解的方法。     

方程族的 Painlev 相容组的求解公式

利用求解Painlevé相容组,本文得到了求解KdV方程族,Kuperschmidt方程族和CDG方程族的Painlevé相容组的递推公式.同时,提供了利用Painlevé相容组寻求孤立子方程族的解的方法.     

一维新的Hamilton可积方程

构造了Loop代数~A_{-1}的一个子代数,利用屠格式导出了一族新的可积孤子方程族,并且是Liouville可积系,具有双Hamilton结构。     

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．     

具有Lenard递推结构之发展方程族的Lax表示

该文对具有Ｌｅｎａｒｄ递推结构的发展方程族，通过转换速推结构为一个算子方程给出了Ｌａｘ表示的一种理论描述．这种描述可应用于各种１＋１维可积系统族Ｌａｘ表示的寻求之中，本文仅就ＫｄＶ可积族和Ａｎｔｏｎｏｗｉｃｚ—Ｆｏｒｄｙ可积族详细阐述了Ｌａｘ表示的具体构造过程．     

一个Bargmann系统与TD族解的对合表示

§1.引言 孤子方程的Lax系统的非线性化方法已成功的用于寻找新的有限维完全可积的系统。本文基于以前的讨论研究与TD特征值问题相联系的非线性保谱演化方程族(TD族)。 TD特征值问题可写为下面等价的形式:     

带两个服务等级的三台机最优在线算法

研究了带服务等级约束的三台平行机在线排序问题.每台机器和每个工件的服务等级为1或者2,工件只能在等级不高于它的机器上加工,即等级为1的工件只能在等级为1的机器上加工,等级为2的工件可在所有机器上加工.每个工件的加工时间为一个单位,目标是极小化所有工件的总完工时间.考虑两种情形:当一台机器等级为1,两台机器等级为2时,给出了竞争比为17/14的最优在线算法;当两台机器等级为1,一台机器等级为2时,给出了竞争比为43/36的最优在线算法.     

一类孤立子系统的Hamilton结构及Liouville可积性

本文给出了一个2×2谱问题及其相应的孤子族,并利用此孤子族的Lenard算子对的性质,证明了该系统是具有Bi-Hamilton结构和Multi-Hamilton结构的广义Hamilton系统,进一步给出其Liouville可积性的证明.此外,值得提出的是此系统可约化为广义TD族、TD族和广义C-KdV族、C-KdV族等,并得到了该孤子族的Hamilton泛函与守恒密度之问的一一对应关系.     

Constructing super D-Kaup-Newell hierarchy and its nonlinear integrable coupling with self-consistent sources

How to construct new super integrable equation hierarchy is an important problem. In this paper, a new Lax pair is proposed and the super D-Kaup-Newell hierarchy is generated, then a nonlinear integrable coupling of the super D-Kaup-Newell hierarchy is constructed. The super Hamiltonian structures of coupling equation hierarchy is derived with the aid of the super variational identity. Finally, the self-consistent sources of super integrable coupling hierarchy is established. It is indicated that this method is a straight- forward and efficient way to construct the super integrable equation hierarchy.     

On the use of the Painlevé property for obtaining miura type transformation

We present a method for obtaining an associated hierarchy of evolution equations possessing the Painlevé property from a given hierarchy which possesses the Painlevé property. This method is applied to the classical Boussinesq hierarchy to obtain the Miura type transformation and the modified classical Boussinesq hierarchy. It is also used to construct a large hierarchy of evolution equations which possess the Painlevé property and include the classical Boussinesq the Jaulent Miodek, the dispersive long wave hierarchy as special cases. All these hierarchies have the same modified hierarchy.The projection supported by the National Natural Science Fundation of China.     

Solving the non-isospectral Ablowitz–Ladik hierarchy via the inverse scattering transform and reductions

The non-isospectral Ablowitz–Ladik hierarchy is integrated by the inverse scattering transform. In contrast with the isospectral Ablowitz–Ladik hierarchy, the eigenvalues of the non-isospectral Ablowitz–Ladik equations in the scattering data are time-dependent. The multi-soliton solution for the hierarchy is presented. The reductions to the non-isospectral discrete NLS hierarchy and the non-isospectral discrete mKdV hierarchy and their solutions are considered.     

A Kind of Discretization of the KdV Hierarchy

We propose a method for introducing higher-order terms in the potential expansion in order to study the continuum limits of the Toda hierarchy. These higher-order terms are differential polynomials in the lower-order terms. This type of potential expansion allows using fewer equations in the Toda hierarchy to recover the KdV hierarchy by the so-called recombination method. We show that the Lax pairs, the Poisson tensors, and the Hamiltonians of the Toda hierarchy tend toward the corresponding objects of the KdV hierarchy in the continuum limit. This method gives a kind of discretization of the KdV hierarchy.     

正互反矩阵一致性的一个充要条件

<正> 层次分析法是一种实用的多维决策方法。在这种分析法中将一个复杂的无结构问题按照属性的不同把它的元素分成若干组,形成互不相交的层次,上一层次的元素对相邻的下一层次     

Symmetric q-Deformed KP Hierarchy

Based on the analytic property of the symmetric q-exponent e_q(x),a new symmetric q-deformed Kadomtsev-Petviashvili(q-KP for short) hierarchy associated with the symmetric q-derivative operator α_q is constructed.Furthermore,the symmetric q-CKP hierarchy and symmetric q-BKP hierarchy are defined.The authors also investigate the additional symmetries of the symmetric q-KP hierarchy.     

Recursion relations for the constrained multi-component KP hierarchy

In this paper, we define a new constrained multi-component KP(cMKP) hierarchy which contains the constrained KP(cKP) hierarchy as a special case. We derive the recursion operator of the constrained multi-component KP hierarchy. As a special example, we also give the recursion operator of the constrained two-component KP hierarchy.     

Refined hierarchy of formulas

In this paper a hierarchy of predicate logic which refines the hierarchy by the number of quantor alterations is introduced and studied. Theorem 1 shows that the hierarchy constructed is the most refined in a certain sense. Theorem 2 describes hierarchy classes in terms of properties of the corresponding models. In Theorems 3 and 4, the connection between the hierarchy of formulas and the hierarchy of sets presented in [1] and the index sets is studied.Translated from Algebra i Logika, Vol. 30, No. 5, pp. 568–582, September–October, 1991.