可积Hamilton系统的拓扑分类理论研究进展

简述了Ｈａｍｉｌｔｏｎ系统理论研究领域中的一个新分支－可积Ｈａｍｉｌｔｏｎ系统的拓扑分类理论的一个侧面，重点阐述了两个自由度Ｈａｍｉｌｔｏｎ系统能量面的拓扑对可积性的影响及其与稳定周期轨道的关系能主一些相关问题。     

模糊数值函数Kaleva积分的刻划及收敛定理

通过定义模糊数绝对值的概念，表明Ｋａｌｅｖａ积分是绝对型的；给出了Ｋａｌｅ－ｖａ积分的几个刻划定理和收敛定理     

A Poisson–Lie Framework for Rational Reductions of the KP Hierarchy

We give a simple proof of I. Krichever's theorem on rational reductions of the Kadomtsev–Petviashvili hierarchy by using the Poisson–Lie structure on the group of pseudo-differential symbols.     

THE BASIC THEORY OF SOLUTIONS OF FUNCTIONAL DIFFERENTIAL EQUATIONS WITH BOUNDED DELAY IN THE SPACE OF INTEGRABLE FUNCTIONS

在可积函数空间中讨论有界滞量泛函微分方程，建立其解的基本理论，包括解的存在性，唯一性及延展性。     

Further examples of integrable systems in two dimensions

The construction of the second constant of motion of second order for two-dimensional classical systems is carried out in terms ofz=q ₁ +iq ₂ andq=q ₁ −iq ₂. As a result a class of Toda-type potentials admitting second order invariants is explored.     

Chandrasekhar H-方程组的可积正解

把ＣｈａｎｄｒａｓｅｋｈａｒＨ方程推广到ＣｈａｎｄｒａｓｅｋｈａｒＨ方程组情形，得到了方程组适定的条件，并在此基础上研究了具有可积正解的必要充分条件和可积正解的稳定性，此外讨论了歧点．     

Global properties of integrable Hamiltonian systems

This paper deals with Lagrangian bundles which are symplectic torus bundles that occur in integrable Hamiltonian systems. We review the theory of obstructions to triviality, in particular monodromy, as well as the ensuing classification problems which involve the Chern and Lagrange class. Our approach, which uses simple ideas from differential geometry and algebraic topology, reveals the fundamental role of the integer affine structure on the base space of these bundles. We provide a geometric proof of the classification of Lagrangian bundles with fixed integer affine structure by their Lagrange class.      

Remark on the well-posedness of the problem of minimization of integral functionals

In this note, we study the well-posedness of the problem of constrained minimization of an integral functional and show that global well-posedness is equivalent to pointwise well-posedness almost everywhere. Our result extends an earlier one by Zolezzi.This research was supported by NSF Grant No. DMS 88-02688.     

Vector NLS solitons interacting with a boundary

We construct multi-soliton solutions of the n-component vector nonlinear Schrödinger equation on the half-line subject to two classes of integrable boundary conditions (BCs): the homogeneous Robin BCs and the mixed Neumann/Dirichlet BCs. The construction is based on the so-called dressing the boundary, which generates soliton solutions by preserving the integrable BCs at each step of the Darboux-dressing process. Under the Robin BCs, examples, including boundary-bound solitons, are explicitly derived; under the mixed Neumann/Dirichlet BCs, the boundary can act as a polarizer that tunes different components of the vector solitons. Connection of our construction to the inverse scattering transform is also provided.     

一个李代数及其相应的可积哈密顿系统

在理论上如何构造更好的可积模型,特别是无穷维哈密顿系统是可积系统研究工作的主要内容之一。本文构造了一个李代数并由此生成相应的圈代数,从而建立了一个适当的等谱问题,利用屠格式得到了一族拉克斯意义下的可积系统,根据迹恒等式得到了这个非线性可积系统的哈密顿结构。