（3＋1）维破碎孤子方程的变量分离解和局域激发模式

多线性分离变量法已成功地应用于诸多（2＋1）维非线性可积系统.将该方法拓展运用于（3＋1）维破碎孤子方程中,获得了含任意函数的变量分离解.通过适当地设定任意函数的形式,得到了（3＋1）维破碎孤子方程丰富的局域激发模式.     

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．     

非线性波动与社会传播混合型方程的整体紧吸引子

本文研究非一波动与神经传播混合型方程ｕｔｔ＝ｕｘｘｔ＋σ（ｕｘ）ｘ－ｈ（ｕ）ｕｔ－ｆ（ｕ）＋ｇ（ｘ）初边值问题的整体吸引子，在σ∈Ｃ＾２，σ（ｓ）〉σ０〉０及ｈ（ｓ）∈Ｃ＾１，－Ｃｏ〈ｈ（ｓ）（０〈Ｃｏ〈λ１／２）且∫ｏ＾ｕｈ（ｓ）ｓｄｓ〈Ｃｕ＾２条件下我们得到了与该方程相应的动力系统整体紧吸引子的存在性，并证明了它具有有限的Ｈａｕｓｄｏｒｆｆｘ维数和ｆｒａｃｔａｌ维数。     

方程f~（n）（x）＝Af~（n－k）（（ax＋b）／（cx－a））

本文提出方程ｆ~（ｎ）（ｘ）＝Ａｆ（ｎ－ｋ）（（ａｘ＋ｂ）／（ｃｘ－ａ）），证明它是可积的．所得结论是文献［１］中结论的推广．     

Modified Boussinesq方程的变量分离

利用和三阶特征值问题相联系的零曲率方程表示理论，本文给出ＭｏｄｉｆｉｅｄＢｏｕｓｓｉｎｅｓｑ方程在显式约束和高阶约束下的两种分解，ＭｏｄｉｆｉｅｄＢｏｕｓｓｉｎｅｅｓｑ方程对ｘ和ｔ的依赖被分解为两个可交换的ｘ－和ｔ－有限维可积的Ｈａｍｉｌｔｏｎ系统．这种分解提供了类似于变量分离的求解方法，通过解两个可交换的有限维可积系统可得到ＭｏｄｉｆｉｅｄＢｏｕｓｓｉｎｅｓｑ方程的某些解．     

二维系统闭轨的不存在性

二维系统闭轨的不存在性周良金（湖北襄阳师范高等专科学校４４１０００）设有二维系统在讨论其闭轨的不存在性时，有充分条件：（ｉ）系统（１）无平衡点；（ⅱ）系统（１）只有一个平衡点，其指数≠＋１；（ｉｉｉ）系统（１）的平衡点任意组合后指数之和都不是＋１；以...     

非线性抛物型方程解的爆破

本文考虑非线性抛物型方程ｕｔ＝ｅｕ（Δｕ＋ｕ），ｘ∈Ω，证明在Ω上当－Δｕ＝λｕ的第一特征值λ１（Ω）＜１时，解ｕ在有限时刻爆破．     

刊外文版9卷2期文章简介(1993)

线性Ｖｏｌｔｅｒｒａ方程存在唯一周期解的充分必要条件王克该文得到了线性Ｖｏｌｔｅｒｒａ方程存在唯一周期解的充分必要条件，并说明了方程（１）具有唯一周期解是它的一个通有性质。ｎ维Ｍｏｂｉｕｓ群的不空方爱农假设ｇ＝［ａｂｃｄ］是Ｃｌｉｆｆｏｒｄ矩阵，ｇ（ｘ）＝（ａｘ＋ｂ）（ｃｘ＋ｄ）－１，作者研究了其不变球体和斜驶、抛物类的更细分类问题，证明了Ｍ（Ｒ２ｋ＋１）中的斜驶元必有不变球体，阐明了Ｌ．Ａｈｆｆｏｒｓ的双曲元的几何意义，引进了强双曲和强抛物类，建立了它们的判别法，作者证明了（－１，２），若ｇ是…     

非线性波动与神经传播混合型方程的整体紧吸引子

本文研究非线性波动与神经传播混合型方程u_tt＝u_xxt＋σ（u_x）_x－h（u）u_t-f（u）＋g（x）初边值问题的整体吸引子.在σ∈C~2,σ＇（s）＞σo＞0及h（s）∈C~1,－Co＜）且∫~u_oh（s）sds＞0）条件下我们得到了与该方程相应的动力系统整体紧吸引子的存在性，并证明了它具有有限的Hausdorff维数和fractal维数．     

Deformation and (3+1)-dimensional integrable model

A suitable and effective deformation relation is derived by using the Miura transformation. In the light of this relation, the (2+1)-dimensional linear heat conductive equation is deformed to a (3+1)-dimensional model. It is proved by standard singularity structure analysis that the (3+1)-dimensional nonlinear equation obtained here is Painlevé integrable.     

A （2＋1）-Dimensional Dispersive Long Wave Hierarchy and its Integrable Couplings

Under the frame of the (2 1)-dimensional zero curvature equation and Tu model, the (2 1)-dimensional dispersive long wave hierarchy is obtained. Furthermore, the loop algebra is expanded into a larger one. Moreover, a class of integrable coupling system for dispersive long wave hierarchy and (2 1)-dimensional multi-component integrable system will be investigated.     

Integrable Models of (1+1)-Dimensional Dilaton Gravity Coupled to Scalar Matter

We describe a class of explicitly integrable models of (1+1)-dimensional dilaton gravity coupled to scalar fields in sufficient detail. The equations of motion of these models reduce to systems of Liouville equations with energy and momentum constraints. We construct the general solution of the equations and constraints in terms of chiral moduli fields explicitly and briefly discuss some extensions of the basic integrable model. These models can be related to higher-dimensional supergravity theories, but we mostly consider them independently of such interpretations. We also briefly review other integrable models of two-dimensional dilaton gravity. __________ Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 146, No. 1, pp. 115–131, January, 2006.     

A topological classification of integrable geodesic flows on the two-dimensional sphere with an additional integral quadratic in the momenta

Summary The analytic expression for a Riemannian metric on a 2-sphere, having integrable geodesic flow with an additional integral quadratic in momenta, is given in [Ko1]. We give the topological classification, up to topological equivalence of Liouville foliations, of all such metrics. The classification is computable, and the formula for calculating the complexity of the flow is straightforward. We prove Fomenko's conjecture that, from the point of view of complexity, the integrable geodesic flows with an additional integral linear or quadratic in momenta exhaust “almost all” integrable geodesic flows on the 2-dimensional sphere.     

Search for high dimensional integrable models

The possible high dimensional integrable models are studied in three different aspects: (i) starting from a strong symmetry operator of a known (1+1) -dimensional integrable model, we can construct a type of (n+1)-dimensional integrable models, high dimensional breaking soliton equations; (ii) from every concrete realization of the generalized Virasoro algebra, we can get many high dimensional integrable models in the meaning that the models possess generalized Virasoro symmetry algebra; (iii) starting from the Schwartz equations which possess conformal invariance, we can also get various high dimensional integrable models in the meaning that they possess Painlevé property. Project supported by the National Natural Science Foundation of China and the Natural Science Foundation of Zhejiang Province.     

Integrable pseudopotentials related to generalized hypergeometric functions

We construct integrable pseudopotentials with an arbitrary number of fields in terms of generalized hypergeometric functions. These pseudopotentials yield some integrable (2 + 1)-dimensional hydrodynamic type systems. In two particular cases these systems are equivalent to integrable scalar 3-dimensional equations of second order. An interesting class of integrable (1 + 1)-dimensional hydrodynamic type systems is also generated by our pseudopotentials.     

Symmetries in (1+1)-dimensional Integrable System with Their Algebraic Structures and Conserved Quantities

In this paper we offer a general method or constructing symmetries and conserved quantities in the (1 + 1)-dimensional integrable system, prove the algebraic relations between symmetries, and what is more, give applications of this method in many integrable systems with physical significance.     

An Example of (3+1)-Dimensional Integrable System

In this paper an example of the (3+1)-dimensional integrable system is considered and the infinite series of divergent forms are described. The classical symmetries for this system, the factor-equation for these symmetries, and exact solutions of this system are found.     

一族包含任意多个未知函数的可积方程组

基于 Lie代数 A1,建立了一个等谱问题 ,由相应的零曲率方程 ,导出一族可积方程组 ,其中未知函数个数可以是任意的