可积系统

一类耦合非线性扩散方程及Liouville完全可积系统

A Hierarchy of Coupled Nonlinear Diffusion Equations and Liouville Completely Integrable Systems

可积系统在微分几何中的某些应用与S～（n+1）中M（？）bius形式为零的超曲面

Some Applications of Integrable Systems in Differential Geometry and Hypersurfaces in S ~( n + 1 ) with Zero M (?) bius Form

在第一部分（第一章）我们给出本文中要用到的关于可积系统的一般背景以及关于CM模型和RS模型研究的最新进展。

Part I ( chapter I ) is a brief introduction of the background for integrable system and newest developments about the CM and RS models .

一个Liouville完全可积系统

A Completely Integrable System in the Liouville Sense

在Reid等人标准型概念的基础上，引进形式可积系统的概念。

Basing on the Reid and others standard form concept of the formal integrable system is led in .

利用可积系统的方法研究3维球空间中的常中曲率（CMC）曲面，并给出了曲面的谱变换。

It is studied that the CMC surfaces in the sphere space of dimension 3 by means of integrable system and its spectral transformation is given .

对称群方法对可用IST方法求解的可积系统的完全分类是一种很有效的方法。

The method of symmetry group is very useful to the complete classification of the sys-tems integrable by IST .

SU（2）与SU（3）自偶Yang-Mills自由源场方程的完全可积系统的研究

Description of the Complete Integrability of the SU ( 2 ) and SU ( 3 ) Self-Dual Yang-Mills Source-Free Field Equations System and Further Discussions

通过对Toda格位势实施标准扰动，得到了一族新的离散可积系统：扰动Toda格系统。

Through standard perturbation of potentials for the Toda lattice hierarchy , the new integrable systems are obtained .

首先给出了C-D对和C-D可积系统的基本理论，然后是具体研究了它们的应用。

Firstly , we give a basic notion and basic theory of C-D pair and C-D integrable system and then we study their applications .

在第一章绪论中，我们简要介绍了近可积系统的相关内容，给出了具五次和导数项的非线性Schr（？）

In chapter 1 , we briefly introduce the near integrable systems , and give the background in physics and the developments in mathematics for the quintic and derivative nonlinear Schrodinger equations .

本文利用离散的零曲率表示的方法构造了几个新的离散的可积系统，并对离散的可积系统的Liouville可积性、无穷多守恒律、可积耦合系统作了研究。

This paper has listed some discrete integrable systems by the discrete zero curvature representation , and , some research such as the Liouville integrability , infinitely many conservation laws and integrable couplings have been investigated .

本文是介绍从Newton运动定理到Hamiltonian可积系统的演化的系列文章的一部分，文中证明了一个关于线性斜对称算子为广义Hamiltonian的一个充分和必要条件。

It demonstrates a necessary and sufficient condition for a linear skew-symmetric operator to be a generalized Hamiltonian . The article aims to provide the readers a good understanding of the development from Newton 's laws of motion to integrable Hamiltonian systems and of the physical world .

通过可积系统的AKNS系统和引入波函数，我们提出了一种从发展方程的已知定态解求新的精确解的方法。

By the AKNS system and introducing the wave function for the integrable equations , a method to find new exact solutions from known stationary solutions of the evolution equations is proposed .

一个经典混沌系统的量子能谱统计分布满足由随机矩阵理论所导出的Winger分布，而可积系统满足无规能谱的统计分布即泊松分布。

It is has been known that the energy spectra statistic of a chaotic system agrees with Wigner distribution which is achieved from Random Matrix Theory and the one of a integrable system is Poisson distribution achieved originally from the irregular spectra .

利用可积系统的思想，借助三维Minkowski空间L3的矩阵模型，研究了L3中具有调和逆平均曲率的类空曲面和洛伦兹调和逆平均曲率类时曲面的可积性及其形变。

Using the matrix models of 3-dimensional Minkowski space , the author applies the integrable system theory to discuss the deformation properties and integrability on the spacelike surfaces with harmonic inverse mean curvature and the timelike surfaces with Lorentz harmonic inverse mean curvature .

利用（2）中构造量子截面图的方法，我们在研究（l）中提到的近可积系统时，发现了经典与量子截面图存在着明显的对应关系。

With the method suggested in ( 2 ) by which we construct quantum sections , when we study the quasi-integrable system , an obvious correspondance between quantum section plots and classical section plots has been found .

可积系统的多孤立子解及其符号计算研究

The Study on Multi-Soliton Solutions of Integrable Systems with Symbolic Computation

确定线性偏微分方程组可积系统的对合特征集方法

On completely integrable system of linear PDEs with involutive characteristic set method

李-陈方程族及与其相联系的经典可积系统

Li-chen 's eigenvalue problem and an associated classical integrable system

对于其中的可积系统，往往是双线性形式。

It is often bilinear form for those integrable systems .

收率可达85%。辛流形与可积系统

The production rate is 85 % . Symplectic Manifold and Integrable Systems

一个二次可积系统在二次保守扰动下的分支

Bifurcation of a Quadratic Integrable System under Quadratic Conservative Perturbations

二维可积系统的求迹公式和周期轨道的量子化

Trace Formula and Periodic Orbits Quantization for Two-Dimensional Integrable System

第四章研究两个连续的超可积系统。

Chapter Four is devoted to the study of two continuous super-integrable systems .

可积系统规则运动的量子经典对应与有关问题

Quantum - classical Correspondence of Regular Motion of Integrable Systems and Related Problems

基于双线性方法的孤子可积系统

Soliton and Integrable Systems Based on Bilinear Method ON THE σ - PRODUCTS

一类三次可积系统在三次扰动下的分支三维动态频谱分析仪

Bifurcation of Cubic Integrable System under Cubic Perturbation ; three-dimensional dynamic spectrum analyser

边界不相关可积系统中无穷多运动积分的研究（Ⅱ）

Infinite Number of Integrals of Motion in Classically Integrable System With Boundary (ⅱ)

本课题主要研究离散可积系统及可积耦合系统。

Discrete integrable systems and its integrable coupling systems are presented in this paper .